Statistics/Basic: Difference between revisions
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{{
[[Statistics|Statistics]] is all about large groups of numbers.
When talking about a set of sampled data, most frequently used is their [[wp:Mean|mean value]] and [[wp:Standard_deviation|standard deviation (stddev)]].
If you have set of data <math>x_i</math> where <math>i = 1, 2, \ldots, n\,\!</math>, the mean is <math>\bar{x}\equiv {1\over n}\sum_i x_i</math>, while the stddev is <math>\sigma\equiv\sqrt{{1\over n}\sum_i \left(x_i - \bar x \right)^2}</math>.
When examining a large quantity of data, one often uses a [[wp:Histogram|histogram]], which shows the counts of data samples falling into a prechosen set of intervals (or bins).
When plotted, often as bar graphs, it visually indicates how often each data value occurs.
'''Task''' Using your language's random number routine, generate real numbers in the range of [0, 1]. It doesn't matter if you chose to use open or closed range.
Create 100 of such numbers (i.e. sample size 100) and calculate their mean and stddev.
Do so for sample size of 1,000 and 10,000, maybe even higher if you feel like.
Show a histogram of any of these sets.
Do you notice some patterns about the standard deviation?
'''Extra''' Sometimes so much data need to be processed that it's impossible to keep all of them at once. Can you calculate the mean, stddev and histogram of a trillion numbers? (You don't really need to do a trillion numbers, just show how it can be done.)
Line 10 ⟶ 18:
;Hint:
For a finite population with equal probabilities at all points, one can derive:
:<math>\overline{(x - \overline{x})^2} = \overline{x^2} - \overline{x}^2</math>
Or, more verbosely:
:<math>
</math>
{{task heading|See also}}
* [[Statistics/Normal_distribution|Statistics/Normal distribution]]
{{Related tasks/Statistical measures}}
<br><hr>
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="11l">F sd_mean(numbers)
V mean = sum(numbers) / numbers.len
V sd = (sum(numbers.map(n -> (n - @mean) ^ 2)) / numbers.len) ^ 0.5
R (sd, mean)
F histogram(numbers)
V h = [0] * 10
V maxwidth = 50
L(n) numbers
h[Int(n * 10)]++
V mx = max(h)
print()
L(i) h
print(‘#.1: #.’.format(L.index / 10, ‘+’ * (i * maxwidth I/ mx)))
print()
L(i) (1, 5)
V n = (0 .< 10 ^ i).map(j -> random:())
print("\n####\n#### #. numbers\n####".format(10 ^ i))
V (sd, mean) = sd_mean(n)
print(‘ sd: #.6, mean: #.6’.format(sd, mean))
histogram(n)</syntaxhighlight>
{{out}}
<pre>
##
## 10 numbers
##
sd: 0.180934, mean: 0.508126
0.0:
0.1:
0.2: +++++++++++++++++++++++++++++++++
0.3: +++++++++++++++++++++++++++++++++
0.4:
0.5: +++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.7:
0.8: ++++++++++++++++
0.9:
##
## 100000 numbers
##
sd: 0.288029, mean: 0.501473
0.0: +++++++++++++++++++++++++++++++++++++++++++++++
0.1: +++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.7: ++++++++++++++++++++++++++++++++++++++++++++++++
0.8: +++++++++++++++++++++++++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++++++++++
</pre>
=={{header|Action!}}==
Calculations on a real Atari 8-bit computer take quite long time. It is recommended to use an emulator capable with increasing speed of Atari CPU.
{{libheader|Action! Tool Kit}}
{{libheader|Action! Real Math}}
<syntaxhighlight lang="action!">INCLUDE "H6:REALMATH.ACT"
DEFINE SIZE="10000"
DEFINE HIST_SIZE="10"
BYTE ARRAY data(SIZE)
CARD ARRAY hist(HIST_SIZE)
PROC Generate()
INT i
FOR i=0 TO SIZE-1
DO
data(i)=Rand(0)
OD
RETURN
PROC CalcMean(INT count REAL POINTER mean)
REAL tmp1,tmp2,r255
INT i
IntToReal(0,mean)
IntToReal(255,r255)
FOR i=0 TO count-1
DO
IntToReal(data(i),tmp1)
RealDiv(tmp1,r255,tmp2)
RealAdd(mean,tmp2,tmp1)
RealAssign(tmp1,mean)
OD
IntToReal(count,tmp1)
RealDiv(mean,tmp1,tmp2)
RealAssign(tmp2,mean)
RETURN
PROC CalcStdDev(INT count REAL POINTER mean,sdev)
REAL tmp1,tmp2,r255
INT i
IntToReal(0,sdev)
IntToReal(255,r255)
FOR i=0 TO count-1
DO
IntToReal(data(i),tmp1)
RealDiv(tmp1,r255,tmp2)
RealSub(tmp2,mean,tmp1)
RealMult(tmp1,tmp1,tmp2)
RealAdd(sdev,tmp2,tmp1)
RealAssign(tmp1,sdev)
OD
IntToReal(count,tmp1)
RealDiv(sdev,tmp1,tmp2)
Sqrt(tmp2,sdev)
RETURN
PROC ClearHistogram()
BYTE i
FOR i=0 TO HIST_SIZE-1
DO
hist(i)=0
OD
RETURN
PROC CalcHistogram(INT count)
INT i,index
ClearHistogram()
FOR i=0 TO count-1
DO
index=data(i)*10/256
hist(index)==+1
OD
RETURN
PROC PrintHistogram()
BYTE i,j,n
INT max
REAL tmp1,tmp2,rmax,rlen
max=0
FOR i=0 TO HIST_SIZE-1
DO
IF hist(i)>max THEN
max=hist(i)
FI
OD
IntToReal(max,rmax)
IntToReal(25,rlen)
FOR i=0 TO HIST_SIZE-1
DO
PrintF("0.%Bx: ",i)
IntToReal(hist(i),tmp1)
RealMult(tmp1,rlen,tmp2)
RealDiv(tmp2,rmax,tmp1)
n=RealToInt(tmp1)
FOR j=0 TO n
DO
Put('*)
OD
PrintF(" %U",hist(i))
IF i<HIST_SIZE-1 THEN
PutE()
FI
OD
RETURN
PROC Test(INT count)
REAL mean,sdev
PrintI(count)
CalcMean(count,mean)
Print(": m=") PrintR(mean)
CalcStdDev(count,mean,sdev)
Print(" sd=") PrintRE(sdev)
CalcHistogram(count)
PrintHistogram()
RETURN
PROC Main()
Put(125) PutE() ;clear screen
MathInit()
Generate()
Test(100)
PutE() PutE()
Test(10000)
RETURN</syntaxhighlight>
{{out}}
[https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Statistics_basic.png Screenshot from Atari 8-bit computer]
<pre>100: m=.5372941127 sd=.2901337976
0.0x: *************** 8
0.1x: ********** 5
0.2x: ************************** 14
0.3x: ***************** 9
0.4x: ***************** 9
0.5x: ************************ 13
0.6x: *************** 8
0.7x: ************** 7
0.8x: ************************** 14
0.9x: ************************ 13
10000: m=.4967046205 sd=.2887503512
0.0x: *********************** 950
0.1x: ************************** 1083
0.2x: ************************* 1054
0.3x: ************************ 998
0.4x: ************************ 975
0.5x: ************************* 1042
0.6x: ************************ 984
0.7x: *********************** 960
0.8x: ************************ 979
0.9x: ************************ 975</pre>
=={{header|Ada}}==
===A plain solution for moderate sample sizes===
<syntaxhighlight lang="ada">with Ada.Text_IO, Ada.Command_Line, Ada.Numerics.Float_Random,
Ada.Numerics.Generic_Elementary_Functions;
procedure Basic_Stat is
package FRG renames Ada.Numerics.Float_Random;
package TIO renames Ada.Text_IO;
type Counter is range 0 .. 2**31-1;
type Result_Array is array(Natural range <>) of Counter;
package FIO is new TIO.Float_IO(Float);
procedure Put_Histogram(R: Result_Array; Scale, Full: Counter) is
begin
for I in R'Range loop
FIO.Put(Float'Max(0.0, Float(I)/10.0 - 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put("..");
FIO.Put(Float'Min(1.0, Float(I)/10.0 + 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put(": ");
for J in 1 .. (R(I)* Scale)/Full loop
Ada.Text_IO.Put("X");
end loop;
Ada.Text_IO.New_Line;
end loop;
end Put_Histogram;
procedure Put_Mean_Et_Al(Sample_Size: Counter;
Val_Sum, Square_Sum: Float) is
Mean: constant Float := Val_Sum / Float(Sample_Size);
package Math is new Ada.Numerics.Generic_Elementary_Functions(Float);
begin
TIO.Put("Mean: ");
FIO.Put(Mean, Fore => 1, Aft => 5, Exp => 0);
TIO.Put(", Standard Deviation: ");
FIO.Put(Math.Sqrt(abs(Square_Sum / Float(Sample_Size)
- (Mean * Mean))), Fore => 1, Aft => 5, Exp => 0);
TIO.New_Line;
end Put_Mean_Et_Al;
N: Counter := Counter'Value(Ada.Command_Line.Argument(1));
Gen: FRG.Generator;
Results: Result_Array(0 .. 10) := (others => 0);
X: Float;
Val_Sum, Squ_Sum: Float := 0.0;
begin
FRG.Reset(Gen);
for I in 1 .. N loop
X := FRG.Random(Gen);
Val_Sum := Val_Sum + X;
Squ_Sum := Squ_Sum + X*X;
declare
Index: Integer := Integer(X*10.0);
begin
Results(Index) := Results(Index) + 1;
end;
end loop;
TIO.Put_Line("After sampling" & Counter'Image(N) & " random numnbers: ");
Put_Histogram(Results, Scale => 600, Full => N);
TIO.New_Line;
Put_Mean_Et_Al(Sample_Size => N, Val_Sum => Val_Sum, Square_Sum => Squ_Sum);
end Basic_Stat;</syntaxhighlight>
{{out}} from a few sample runs:
<pre>> ./basic_stat 1000
After sampling 1000 random numnbers:
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXX
Mean: 0.48727, Standard Deviation: 0.28502
> ./basic_stat 10_000
After sampling 10000 random numnbers:
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Mean: 0.50096, Standard Deviation: 0.28869
> ./basic_stat 100_000
After sampling 100000 random numnbers:
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Mean: 0.50178, Standard Deviation: 0.28805</pre>
===Making the solution ready for one trillion samples===
Depending on where you live, one trillion is either 10^12 or 10^18 [https://en.wikipedia.org/wiki/Trillion].
Below, I'll assume 10^12, which implies a number of operations I can still perform on my PC.
The above program will fail with such large inputs for two reasons:
1. The type Counter cannot hold such large numbers.
2. The variables Val_Sum and Squ_Sum will numerically fail, because the type Float only provides about six decimal digits of accuracy. I.e., at some point, Val_Sum and (a little bit later) Squ_Sum are so large that adding a value below 1 has no effect, any more.
To make the program ready for sample size 10^12, we modify it as follows.
1. Change the type Counter to hold such large numbers.
2. Define a type High_Precision, that will hold (at least) 15 decimal digits. Define Val_Sum and Squ_Sum as being from that type. Include the neccessary type conversions.
3. Provide some progress report, during the running time.
This is the modified program
<syntaxhighlight lang="ada">with Ada.Text_IO, Ada.Command_Line, Ada.Numerics.Float_Random,
Ada.Numerics.Generic_Elementary_Functions;
procedure Long_Basic_Stat is
package FRG renames Ada.Numerics.Float_Random;
package TIO renames Ada.Text_IO;
type Counter is range 0 .. 2**63-1;
type Result_Array is array(Natural range <>) of Counter;
type High_Precision is digits 15;
package FIO is new TIO.Float_IO(Float);
procedure Put_Histogram(R: Result_Array; Scale, Full: Counter) is
begin
for I in R'Range loop
FIO.Put(Float'Max(0.0, Float(I)/10.0 - 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put("..");
FIO.Put(Float'Min(1.0, Float(I)/10.0 + 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put(": ");
for J in 1 .. (R(I)* Scale)/Full loop
Ada.Text_IO.Put("X");
end loop;
Ada.Text_IO.New_Line;
end loop;
end Put_Histogram;
procedure Put_Mean_Et_Al(Sample_Size: Counter;
Val_Sum, Square_Sum: Float) is
Mean: constant Float := Val_Sum / Float(Sample_Size);
package Math is new Ada.Numerics.Generic_Elementary_Functions(Float);
begin
TIO.Put("Mean: ");
FIO.Put(Mean, Fore => 1, Aft => 5, Exp => 0);
TIO.Put(", Standard Deviation: ");
FIO.Put(Math.Sqrt(abs(Square_Sum / Float(Sample_Size)
- (Mean * Mean))), Fore => 1, Aft => 5, Exp => 0);
TIO.New_Line;
end Put_Mean_Et_Al;
N: Counter := Counter'Value(Ada.Command_Line.Argument(1));
Gen: FRG.Generator;
Results: Result_Array(0 .. 10) := (others => 0);
X: Float;
Val_Sum, Squ_Sum: High_Precision := 0.0;
begin
FRG.Reset(Gen);
for Outer in 1 .. 1000 loop
for I in 1 .. N/1000 loop
X := FRG.Random(Gen);
Val_Sum := Val_Sum + High_Precision(X);
Squ_Sum := Squ_Sum + High_Precision(X)*High_Precision(X);
declare
Index: Integer := Integer(X*10.0);
begin
Results(Index) := Results(Index) + 1;
end;
end loop;
if Outer mod 50 = 0 then
TIO.New_Line(1);
TIO.Put_Line(Integer'Image(Outer/10) &"% done; current results:");
Put_Mean_Et_Al(Sample_Size => (Counter(Outer)*N)/1000,
Val_Sum => Float(Val_Sum),
Square_Sum => Float(Squ_Sum));
else
Ada.Text_IO.Put(".");
end if;
end loop;
TIO.New_Line(4);
TIO.Put_Line("After sampling" & Counter'Image(N) & " random numnbers: ");
Put_Histogram(Results, Scale => 600, Full => N);
TIO.New_Line;
Put_Mean_Et_Al(Sample_Size => N,
Val_Sum => Float(Val_Sum), Square_Sum => Float(Squ_Sum));
end Long_Basic_Stat;</syntaxhighlight>
{{out}} for sample size 10^12 took one night on my PC:
<pre>.................................................
5% done; current results:
Mean: 0.50000, Standard Deviation: 0.28867
.................................................
10% done; current results:
Mean: 0.50000, Standard Deviation: 0.28867
.................................................
15% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
20% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
25% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
30% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
35% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
40% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
45% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
50% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
55% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
60% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
65% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
70% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
75% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
80% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
85% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
90% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
95% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
.................................................
100% done; current results:
Mean: 0.50000, Standard Deviation: 0.28868
After sampling 1000000000000 random numnbers:
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
Mean: 0.50000, Standard Deviation: 0.28868</pre>
The same program should still work fine for sample size 10^18, but I'll need my PC in the meantime. ;-)
=={{header|ALGOL 68}}==
Suitable for the moderate sample sizes millions or billions probably - not suitable for e.g.: a trillion samples (with early 21st century hardware).
<syntaxhighlight lang="algol68">
BEGIN # calculate the mean and standard deviation of some data and draw a #
# histogram of the data #
# return the mean of data #
OP MEAN = ( []REAL data )REAL:
IF INT len = ( UPB data - LWB data ) + 1;
len < 1
THEN 0
ELSE REAL sum := 0;
FOR i FROM LWB data TO UPB data DO
sum +:= data[ i ]
OD;
sum / len
FI # MEAN # ;
# returns the standard deviation of data #
OP STDDEV = ( []REAL data )REAL:
IF INT len = ( UPB data - LWB data ) + 1;
len < 1
THEN 0
ELSE REAL m = MEAN data;
REAL sum := 0;
FOR i FROM LWB data TO UPB data DO
sum +:= ( data[ i ] - m ) ^ 2
OD;
sqrt( sum / len )
FI # STDDEV # ;
# generates a row of n random numbers in the range [0..1) #
PROC random row = ( INT n )REF[]REAL:
BEGIN
REF[]REAL data = HEAP[ 1 : n ]REAL;
FOR i TO n DO
data[ i ] := next random
OD;
data
END # random row # ;
# returns s right-padded with spaces to at least w characters #
PROC right pad = ( STRING s, INT w )STRING:
IF INT len = ( UPB s - LWB s ) + 1; len >= w THEN s ELSE s + ( " " * ( w - len ) ) FI;
# prints a histogram of data ( assumed to be in [0..1) ) with n bars #
# scaled to fit in h scale characters #
PROC print histogram = ( []REAL data, INT n, h scale )VOID:
IF n > 0 AND h scale > 0 THEN
[ 0 : n - 1 ]INT count;
FOR i FROM LWB count TO UPB count DO count[ i ] := 0 OD;
FOR i FROM LWB data TO UPB data DO
count[ ENTIER ( data[ i ] * n ) ] +:= 1
OD;
INT max count := 0;
FOR i FROM LWB count TO UPB count DO
IF count[ i ] > max count THEN max count := count[ i ] FI
OD;
INT len = ( UPB data - LWB data ) + 1;
REAL v := 0;
REAL scale = max count / h scale;
FOR i FROM LWB count TO UPB count DO
print( ( fixed( v, -4, 2 ), ": " ) );
print( ( right pad( "=" * ROUND ( count[ i ] / scale ), h scale ) ) );
print( ( " (", whole( count[ i ], 0 ), ")", newline ) );
v +:= 1 / n
OD
FI # print histogram # ;
# task #
# generate n random data items, calculate the mean and stddev and show #
# a histogram of the data #
PROC show statistics = ( INT n )VOID:
BEGIN
[]REAL data = random row( n );
print( ( "Sample size: ", whole( n, -6 ) ) );
print( ( ", mean: ", fixed( MEAN data, -8, 4 ) ) );
print( ( ", stddev: ", fixed( STDDEV data, -8, 4 ) ) );
print( ( newline ) );
print histogram( data, 10, 32 );
print( ( newline ) )
END # show statistics # ;
show statistics( 100 );
show statistics( 1 000 );
show statistics( 10 000 );
show statistics( 100 000 )
END
</syntaxhighlight>
{{out}}
<pre>
Sample size: 100, mean: 0.5092, stddev: 0.2783
0.00: ==================== (10)
0.10: ==================== (10)
0.20: ========== (5)
0.30: ======================== (12)
0.40: ======================== (12)
0.50: ================ (8)
0.60: ================================ (16)
0.70: ================ (8)
0.80: ======================== (12)
0.90: ============== (7)
Sample size: 1000, mean: 0.4989, stddev: 0.2855
0.00: ========================== (92)
0.10: =============================== (110)
0.20: =========================== (97)
0.30: ============================ (100)
0.40: ============================ (102)
0.50: ========================== (94)
0.60: ================================ (115)
0.70: ========================== (92)
0.80: =========================== (98)
0.90: ============================ (100)
Sample size: 10000, mean: 0.5011, stddev: 0.2863
0.00: ============================= (942)
0.10: ============================== (996)
0.20: ================================ (1057)
0.30: ============================= (968)
0.40: =============================== (1028)
0.50: ============================== (1000)
0.60: =============================== (1008)
0.70: =============================== (1019)
0.80: ============================== (1003)
0.90: ============================== (979)
Sample size: 100000, mean: 0.4996, stddev: 0.2881
0.00: =============================== (9917)
0.10: ================================ (10136)
0.20: =============================== (9936)
0.30: =============================== (9850)
0.40: ================================ (10123)
0.50: ================================ (10139)
0.60: ================================ (10167)
0.70: =============================== (9840)
0.80: =============================== (9905)
0.90: =============================== (9987)
</pre>
=={{header|Amazing Hopper}}==
<syntaxhighlight lang="c">
#include <basico.h>
#define TOTAL_BINES 10
algoritmo
/* verifica y obtiene argumento: tamaño de muestra*/
tamaño muestra=0
//obtener total argumentos
//es distinto a '2', entonces{ terminar }
//obtener parámetro numérico(2), mover a 'tamaño muestra'
/* algo menos natural, pero más claro para una mente formal: */
obtener total argumentos
si ' es distinto a( 2 ) '
terminar
sino
guardar ' parám numérico(2)' en 'tamaño muestra'
fin si
/* establece la escala para desplegar barras */
escala = 1.0
si ' #(tamaño muestra > 50) '
#( escala = 50.0 / tamaño muestra )
fin si
/* Generar muestra de tamaño "tamaño muestra" */
dimensionar con ( tamaño muestra) matriz aleatoria entera ( 10, muestra )
decimales '3'
/* Genera tabla de clases con 10 bines */
tabla de clases=0
bines(TOTAL_BINES, muestra), mover a 'tabla de clases'
/* Imprime tabla de clases */
ir a subrutina( desplegar tabla de clases)
/* Calcula promedio según tabla de clases */
promedio tabla=0, FREC=0, MC=0
ir a subrutina ( calcular promedio de tabla de clases )
/* Calcula desviación estándar y varianza */
desviación estándar=0, varianza=0
ir a subrutina ( calcular desviación estándar y varianza )
/* Calcula promedio de la muestra completa e imprime medidas */
ir a subrutina ( desplegar medidas y medias )
/* Construye barras */
tamaño barras=0, barras=0
ir a subrutina( construir barras para histograma ), mover a 'barras'
/* arma histograma de salida */
sMC=0
ir a subrutina( construir y desplegar histograma )
terminar
subrutinas
desplegar tabla de clases:
token.separador '"\t"'
imprimir '#(utf8("Tamaño de la muestra = ")), tamaño muestra,NL,NL,\
#(utf8("Números entre 0 y 10\n\n")),\
" --RANGO--\tM.DE C.\tFREC.\tF.R\t F.A.\tF.R.A.\n",\
"-----------------------------------------------------\n"'
imprimir 'justificar derecha(5,#(string(tabla de clases))), NL'
retornar
desplegar medidas y medias:
promedio muestra=0
muestra, promediar, mover a 'promedio muestra'
imprimir ' "Media de la muestra = ", promedio muestra, NL,\
"Media de la tabla = ", promedio tabla, NL,\
"Varianza = ", varianza, NL,\
#(utf8("Desviación estandar = ")), desviación estándar,NL'
retornar
construir barras para histograma:
#(tamaño barras = int(FREC * escala * 5))
dimensionar con (TOTAL_BINES) matriz rellena ("*", barras)
#(barras = replicate( barras, tamaño barras))
retornar ' barras '
construir y desplegar histograma:
#(sMC = string(MC))
unir columnas( sMC, sMC, justificar derecha(5,#(string(FREC))), barras )
/* Imprime histograma */
token.separador '" "'
imprimir ( " M.C. FREC.\n-----------\n",\
sMC,NL )
retornar
calcular promedio de tabla de clases:
//[1:filasde(tabla de clases), 3] coger (tabla de clases), mover a 'MC'
//[1:filasde(tabla de clases), 4] coger (tabla de clases), mover a 'FREC'
/* un poco menos natural, pero más claro para una mente formal: */
#basic{
MC = tabla de clases[ 1:TOTAL_BINES, 3]
FREC = tabla de clases[ 1:TOTAL_BINES, 4]
}
borrar intervalo
multiplicar(MC,FREC), calcular sumatoria, dividir entre (tamaño muestra),
mover a 'promedio tabla'
retornar
calcular desviación estándar y varianza:
restar( MC, promedio tabla), elevar al cuadrado, por (FREC),
calcular sumatoria, dividir entre(tamaño muestra), copiar en 'varianza'
calcular raíz, mover a 'desviación estándar'
retornar
</syntaxhighlight>
{{out}}
<pre>
$ hopper3 basica/estat.bas 100
Tamaño de la muestra = 100
Números entre 0 y 10
--RANGO-- M.DE C. FREC. F.R F.A. F.R.A.
-----------------------------------------------------
0 1 0.500 12 0.120 12 0.120
1 2 1.500 7 0.070 19 0.190
2 3 2.500 9 0.090 28 0.280
3 4 3.500 14 0.140 42 0.420
4 5 4.500 14 0.140 56 0.560
5 6 5.500 3 0.030 59 0.590
6 7 6.500 8 0.080 67 0.670
7 8 7.500 11 0.110 78 0.780
8 9 8.500 7 0.070 85 0.850
9 10 9.500 15 0.150 100 1.000
Media de la muestra = 4.540
Media de la tabla = 5.040
Varianza = 8.969
Desviación estandar = 2.995
M.C. FREC.
-----------
0.500 12 ******************************
1.500 7 *****************
2.500 9 **********************
3.500 14 ***********************************
4.500 14 ***********************************
5.500 3 *******
6.500 8 ********************
7.500 11 ***************************
8.500 7 *****************
9.500 15 *************************************
$ hopper3 basica/estat.bas 1000
Tamaño de la muestra = 1000
Números entre 0 y 10
--RANGO-- M.DE C. FREC. F.R F.A. F.R.A.
-----------------------------------------------------
0 1 0.500 87 0.087 87 0.087
1 2 1.500 94 0.094 181 0.181
2 3 2.500 109 0.109 290 0.290
3 4 3.500 109 0.109 399 0.399
4 5 4.500 95 0.095 494 0.494
5 6 5.500 99 0.099 593 0.593
6 7 6.500 91 0.091 684 0.684
7 8 7.500 100 0.100 784 0.784
8 9 8.500 106 0.106 890 0.890
9 10 9.500 110 0.110 1000 1.000
Media de la muestra = 4.598
Media de la tabla = 5.098
Varianza = 8.235
Desviación estandar = 2.870
M.C. FREC.
-----------
0.500 87 *********************
1.500 94 ***********************
2.500 109 ***************************
3.500 109 ***************************
4.500 95 ***********************
5.500 99 ************************
6.500 91 **********************
7.500 100 *************************
8.500 106 **************************
9.500 110 ***************************
$ hopper3 basica/estat.bas 10000
Tamaño de la muestra = 10000
Números entre 0 y 10
--RANGO-- M.DE C. FREC. F.R F.A. F.R.A.
-----------------------------------------------------
0 1 0.500 1039 0.104 1039 0.104
1 2 1.500 1014 0.101 2053 0.205
2 3 2.500 1005 0.101 3058 0.306
3 4 3.500 976 0.098 4034 0.403
4 5 4.500 949 0.095 4983 0.498
5 6 5.500 995 0.100 5978 0.598
6 7 6.500 1039 0.104 7017 0.702
7 8 7.500 1009 0.101 8026 0.803
8 9 8.500 992 0.099 9018 0.902
9 10 9.500 982 0.098 10000 1.000
Media de la muestra = 4.479
Media de la tabla = 4.979
Varianza = 8.310
Desviación estandar = 2.883
M.C. FREC.
-----------
0.500 1039 *************************
1.500 1014 *************************
2.500 1005 *************************
3.500 976 ************************
4.500 949 ***********************
5.500 995 ************************
6.500 1039 *************************
7.500 1009 *************************
8.500 992 ************************
9.500 982 ************************
$ hopper3 basica/estat.bas 100000
Tamaño de la muestra = 100000
Números entre 0 y 10
--RANGO-- M.DE C. FREC. F.R F.A. F.R.A.
-----------------------------------------------------
0 1 0.500 10139 0.101 10139 0.101
1 2 1.500 10025 0.100 20164 0.202
2 3 2.500 9990 0.100 30154 0.302
3 4 3.500 10021 0.100 40175 0.402
4 5 4.500 9880 0.099 50055 0.501
5 6 5.500 10054 0.101 60109 0.601
6 7 6.500 9961 0.100 70070 0.701
7 8 7.500 10144 0.101 80214 0.802
8 9 8.500 9773 0.098 89987 0.900
9 10 9.500 10013 0.100 100000 1.000
Media de la muestra = 4.489
Media de la tabla = 4.989
Varianza = 8.264
Desviación estandar = 2.875
M.C. FREC.
-----------
0.500 10139 **************************************************
1.500 10025 **************************************************
2.500 9990 *************************************************
3.500 10021 **************************************************
4.500 9880 *************************************************
5.500 10054 **************************************************
6.500 9961 *************************************************
7.500 10144 **************************************************
8.500 9773 ************************************************
9.500 10013 **************************************************
</pre>
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
{{works with|Chipmunk Basic}}
{{works with|GW-BASIC}}
{{works with|MSX BASIC}}
{{trans|Chipmunk Basic}}
<syntaxhighlight lang="qbasic">100 HOME : rem 100 CLS for Chipmunk Basic, GW-BASIC and MSX BASIC
110 CLEAR : n = 100 : GOSUB 150 : rem no se requiere CLEAR
120 CLEAR : n = 1000 : GOSUB 150
130 CLEAR : n = 10000 : GOSUB 150
140 END
150 rem SUB sample(n)
160 DIM samp(n)
170 FOR i = 1 TO n
180 samp(i) = RND(1)
190 NEXT i
200 rem calculate mean, standard deviation
210 sum = 0
220 sumsq = 0
230 FOR i = 1 TO n
240 sum = sum+samp(i)
250 sumsq = sumsq+samp(i)^2
260 NEXT i
270 PRINT "Sample size ";n
280 mean = sum/n
290 PRINT
300 PRINT " Mean = ";mean
310 PRINT " Std Dev = ";(sumsq/n-mean^2)^0.5
320 PRINT
330 rem------- Show histogram
340 scal = 10
350 DIM bins(scal)
360 FOR i = 1 TO n
370 z = INT(scal*samp(i))
380 bins(z) = bins(z)+1
390 NEXT i
400 FOR b = 0 TO scal-1
410 PRINT " ";b;" : ";
420 FOR j = 1 TO INT(scal*bins(b))/n*70
430 PRINT "*";
440 NEXT j
450 PRINT
460 NEXT b
470 PRINT
480 RETURN</syntaxhighlight>
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{works with|QBasic}}
{{trans|Yabasic}}
<syntaxhighlight lang="qbasic">100 sub sample(n)
110 dim samp(n)
120 for i = 1 to n
130 samp(i) = rnd(1)
140 next i
150 rem calculate mean, standard deviation
160 sum = 0
170 sumsq = 0
180 for i = 1 to n
190 sum = sum+samp(i)
200 sumsq = sumsq+samp(i)^2
210 next i
220 print "Sample size ";n
230 mean = sum/n
240 print
250 print " Mean = ";mean
260 print " Std Dev = ";(sumsq/n-mean^2)^0.5
270 print
280 rem------- Show histogram
290 scal = 10
300 dim bins(scal)
310 for i = 1 to n
320 z = int(scal*samp(i))
330 bins(z) = bins(z)+1
340 next i
350 for b = 0 to scal-1
360 print " ";b;" : ";
370 for j = 1 to int(scal*bins(b))/n*70
380 print "*";
390 next j
400 print
410 next b
420 print
430 end sub
440 cls
450 sample(100)
460 sample(1000)
470 sample(10000)
480 end</syntaxhighlight>
==={{header|FreeBASIC}}===
<syntaxhighlight lang="freebasic">' FB 1.05.0 Win64
Randomize
Sub basicStats(sampleSize As Integer)
If sampleSize < 1 Then Return
Dim r(1 To sampleSize) As Double
Dim h(0 To 9) As Integer '' all zero by default
Dim sum As Double = 0.0
Dim hSum As Integer = 0
' Generate 'sampleSize' random numbers in the interval [0, 1)
' calculate their sum
' and in which box they will fall when drawing the histogram
For i As Integer = 1 To sampleSize
r(i) = Rnd
sum += r(i)
h(Int(r(i) * 10)) += 1
Next
For i As Integer = 0 To 9 : hSum += h(i) : Next
' adjust one of the h() values if necessary to ensure hSum = sampleSize
Dim adj As Integer = sampleSize - hSum
If adj <> 0 Then
For i As Integer = 0 To 9
h(i) += adj
If h(i) >= 0 Then Exit For
h(i) -= adj
Next
End If
Dim mean As Double = sum / sampleSize
Dim sd As Double
sum = 0.0
' Now calculate their standard deviation
For i As Integer = 1 To sampleSize
sum += (r(i) - mean) ^ 2.0
Next
sd = Sqr(sum/sampleSize)
' Draw a histogram of the data with interval 0.1
Dim numStars As Integer
' If sample size > 500 then normalize histogram to 500
Dim scale As Double = 1.0
If sampleSize > 500 Then scale = 500.0 / sampleSize
Print "Sample size "; sampleSize
Print
Print Using " Mean #.######"; mean;
Print Using " SD #.######"; sd
Print
For i As Integer = 0 To 9
Print Using " #.## : "; i/10.0;
Print Using "##### " ; h(i);
numStars = Int(h(i) * scale + 0.5)
Print String(numStars, "*")
Next
End Sub
basicStats 100
Print
basicStats 1000
Print
basicStats 10000
Print
basicStats 100000
Print
Print "Press any key to quit"
Sleep</syntaxhighlight>
{{out}}
<pre>Sample size 100
Mean 0.485580 SD 0.269003
0.00 : 7 *******
0.10 : 10 **********
0.20 : 12 ************
0.30 : 17 *****************
0.40 : 8 ********
0.50 : 10 **********
0.60 : 11 ***********
0.70 : 9 *********
0.80 : 9 *********
0.90 : 7 *******
Sample size 1000
Mean 0.504629 SD 0.292029
0.00 : 99 **************************************************
0.10 : 99 **************************************************
0.20 : 93 ***********************************************
0.30 : 108 ******************************************************
0.40 : 101 ***************************************************
0.50 : 97 *************************************************
0.60 : 90 *********************************************
0.70 : 110 *******************************************************
0.80 : 102 ***************************************************
0.90 : 101 ***************************************************
Sample size 10000
Mean 0.500027 SD 0.290618
0.00 : 1039 ****************************************************
0.10 : 997 **************************************************
0.20 : 978 *************************************************
0.30 : 988 *************************************************
0.40 : 998 **************************************************
0.50 : 959 ************************************************
0.60 : 1037 ****************************************************
0.70 : 1004 **************************************************
0.80 : 965 ************************************************
0.90 : 1035 ****************************************************
Sample size 100000
Mean 0.499503 SD 0.288730
0.00 : 10194 ***************************************************
0.10 : 9895 *************************************************
0.20 : 9875 *************************************************
0.30 : 9922 **************************************************
0.40 : 10202 ***************************************************
0.50 : 9981 **************************************************
0.60 : 10034 **************************************************
0.70 : 10012 **************************************************
0.80 : 9957 **************************************************
0.90 : 9928 **************************************************</pre>
==={{header|GW-BASIC}}===
{{works with|Applesoft BASIC}}
{{works with|Chipmunk Basic}}
{{works with|PC-BASIC|any}}
{{works with|MSX BASIC}}
{{trans|Chipmunk Basic}}
<syntaxhighlight lang="qbasic">100 CLS : rem 100 HOME FOR Applesoft BASIC
110 CLEAR : n = 100 : GOSUB 150
120 CLEAR : n = 1000 : GOSUB 150
130 CLEAR : n = 10000 : GOSUB 150
140 END
150 rem SUB sample(n)
160 DIM samp(n)
170 FOR i = 1 TO n
180 samp(i) = RND(1)
190 NEXT i
200 rem calculate mean, standard deviation
210 sum = 0
220 sumsq = 0
230 FOR i = 1 TO n
240 sum = sum+samp(i)
250 sumsq = sumsq+samp(i)^2
260 NEXT i
270 PRINT "Sample size ";n
280 mean = sum/n
290 PRINT
300 PRINT " Mean = ";mean
310 PRINT " Std Dev = ";(sumsq/n-mean^2)^0.5
320 PRINT
330 rem------- Show histogram
340 scal = 10
350 DIM bins(scal)
360 FOR i = 1 TO n
370 z = INT(scal*samp(i))
380 bins(z) = bins(z)+1
390 NEXT i
400 FOR b = 0 TO scal-1
410 PRINT " ";b;" : ";
420 FOR j = 1 TO INT(scal*bins(b))/n*70
430 PRINT "*";
440 NEXT j
450 PRINT
460 NEXT b
470 PRINT
480 RETURN</syntaxhighlight>
==={{header|Liberty BASIC}}===
Be aware that the PRNG in LB has a SLIGHT bias.
<syntaxhighlight lang="lb">call sample 100
call sample 1000
call sample 10000
end
sub sample n
dim dat( n)
for i =1 to n
dat( i) =rnd( 1)
next i
'// show mean, standard deviation
sum =0
sSq =0
for i =1 to n
sum =sum +dat( i)
sSq =sSq +dat( i)^2
next i
print n; " data terms used."
mean =sum / n
print "Mean ="; mean
print "Stddev ="; ( sSq /n -mean^2)^0.5
'// show histogram
nBins =10
dim bins( nBins)
for i =1 to n
z =int( nBins *dat( i))
bins( z) =bins( z) +1
next i
for b =0 to nBins -1
for j =1 to int( nBins *bins( b)) /n *70)
print "#";
next j
print
next b
print
end sub</syntaxhighlight>
{{out}}
<pre> 100000 data terms used.
Mean =0.49870232
Stddev =0.28926563
######################################################################
######################################################################
######################################################################
######################################################################
#####################################################################
#####################################################################
#####################################################################
#####################################################################
######################################################################
#####################################################################</pre>
==={{header|MSX Basic}}===
The [[#GW-BASIC|GW-BASIC]] solution works without any changes.
==={{header|PureBasic}}===
{{trans|Liberty BASIC}}
Changes were made from the Liberty BASIC version to normalize the histogram as well as implement a random float function.
<syntaxhighlight lang="purebasic">Procedure.f randomf()
#RNG_max_resolution = 2147483647
ProcedureReturn Random(#RNG_max_resolution) / #RNG_max_resolution
EndProcedure
Procedure sample(n)
Protected i, nBins, binNumber, tickMarks, maxBinValue
Protected.f sum, sumSq, mean
Dim dat.f(n)
For i = 1 To n
dat(i) = randomf()
Next
;show mean, standard deviation
For i = 1 To n
sum + dat(i)
sumSq + dat(i) * dat(i)
Next i
PrintN(Str(n) + " data terms used.")
mean = sum / n
PrintN("Mean =" + StrF(mean))
PrintN("Stddev =" + StrF((sumSq / n) - Sqr(mean * mean)))
;show histogram
nBins = 10
Dim bins(nBins)
For i = 1 To n
binNumber = Int(nBins * dat(i))
bins(binNumber) + 1
Next
maxBinValue = 1
For i = 0 To nBins
If bins(i) > maxBinValue
maxBinValue = bins(i)
EndIf
Next
#normalizedMaxValue = 70
For binNumber = 0 To nBins
tickMarks = Int(bins(binNumber) * #normalizedMaxValue / maxBinValue)
PrintN(ReplaceString(Space(tickMarks), " ", "#"))
Next
PrintN("")
EndProcedure
If OpenConsole()
sample(100)
sample(1000)
sample(10000)
Print(#CRLF$ + #CRLF$ + "Press ENTER to exit"): Input()
CloseConsole()
EndIf</syntaxhighlight>
{{out}}
<pre>100 data terms used.
Mean =0.4349198639
Stddev =-0.1744846404
#########################################################
#########################################
################################
#################################################################
################################
#####################################################
######################################################################
################
########################
################
1000 data terms used.
Mean =0.4960154891
Stddev =-0.1691310555
###############################################################
#######################################################
#############################################################
######################################################################
##########################################################
##############################################################
####################################################################
###############################################################
#############################################################
#####################################################
10000 data terms used.
Mean =0.5042046309
Stddev =-0.1668083966
##################################################################
################################################################
##################################################################
####################################################################
################################################################
######################################################################
####################################################################
###################################################################
####################################################################
####################################################################</pre>
==={{header|QBasic}}===
{{works with|QBasic|1.1}}
{{works with|QuickBasic|4.5}}
{{trans|Yabasic}}
<syntaxhighlight lang="qbasic">SUB sample (n)
DIM samp(n)
FOR i = 1 TO n
samp(i) = RND(1)
NEXT i
REM calculate mean, standard deviation
sum = 0
sumsq = 0
FOR i = 1 TO n
sum = sum + samp(i)
sumsq = sumsq + samp(i) ^ 2
NEXT i
PRINT "Sample size "; n
mean = sum / n
PRINT
PRINT " Mean = "; mean
PRINT " Std Dev = "; (sumsq / n - mean ^ 2) ^ .5
PRINT
REM------- Show histogram
scal = 10
DIM bins(scal)
FOR i = 1 TO n
z = INT(scal * samp(i))
bins(z) = bins(z) + 1
NEXT i
FOR b = 0 TO scal - 1
PRINT " "; b; " : ";
FOR j = 1 TO INT(scal * bins(b)) / n * 70
PRINT "*";
NEXT j
PRINT
NEXT b
PRINT
END SUB
CLS
sample (100)
sample (1000)
sample (10000)
END</syntaxhighlight>
==={{header|Run BASIC}}===
<syntaxhighlight lang="runbasic">call sample 100
call sample 1000
call sample 10000
end
sub sample n
dim samp(n)
for i =1 to n
samp(i) =rnd(1)
next i
' calculate mean, standard deviation
sum = 0
sumSq = 0
for i = 1 to n
sum = sum + samp(i)
sumSq = sumSq + samp(i)^2
next i
print n; " Samples used."
mean = sum / n
print "Mean = "; mean
print "Std Dev = "; (sumSq /n -mean^2)^0.5
'------- Show histogram
bins = 10
dim bins(bins)
for i = 1 to n
z = int(bins * samp(i))
bins(z) = bins(z) +1
next i
for b = 0 to bins -1
print b;" ";
for j = 1 to int(bins *bins(b)) /n *70
print "*";
next j
print
next b
print
end sub</syntaxhighlight>
<pre style="height: 40ex; overflow: scroll">
100 Samples used.
Mean = 0.514312738
Std Dev = 0.291627558
0 **************************************************************************************************
1 **********************************************************************
2 *********************
3 ***********************************
4 ***************************************************************
5 *******************************************************************************************
6 ***********************************************************************************************************************
7 **********************************************************************
8 ***************************************************************
9 **********************************************************************
1000 Samples used.
Mean = 0.495704208
Std Dev = 0.281389168
0 ***************************************************************
1 ********************************************************************
2 **************************************************************************
3 *******************************************************************************
4 **************************************************************************
5 **********************************************************************
6 ************************************************************************
7 **********************************************************************
8 ********************************************************
9 **********************************************************************
10000 Samples used.
Mean = 0.493594211
Std Dev = 0.288635912
0 ************************************************************************
1 ************************************************************************
2 **********************************************************************
3 *******************************************************************
4 **********************************************************************
5 ************************************************************************
6 ************************************************************************
7 *****************************************************************
8 **********************************************************************
9 ******************************************************************</pre>
==={{header|Yabasic}}===
{{trans|Run BASIC}}
<syntaxhighlight lang="vb">sample ( 100)
sample ( 1000)
sample (10000)
end
sub sample (n)
dim samp(n)
for i = 1 to n
samp(i) = ran(1)
next i
// calculate mean, standard deviation
sum = 0
sumSq = 0
for i = 1 to n
sum = sum + samp(i)
sumSq = sumSq + samp(i) ^ 2
next i
print "Sample size ", n
mean = sum / n
print "\n Mean = ", mean
print " Std Dev = ", (sumSq / n - mean ^ 2) ^ 0.5
print
//------- Show histogram
bins = 10
dim bins(bins)
for i = 1 to n
z = int(bins * samp(i))
bins(z) = bins(z) + 1
next i
for b = 0 to bins -1
print " ", b, " : ";
for j = 1 to int(bins * bins(b)) / n * 70
print "*";
next j
print
next b
print
end sub</syntaxhighlight>
=={{header|C}}==
Sample code.
<
#include <stdlib.h>
#include <math.h>
Line 118 ⟶ 1,676:
}
}
}</
=={{header|C sharp|C#}}==
{{libheader|Math.Net}}
<syntaxhighlight lang="csharp">using System;
using MathNet.Numerics.Statistics;
class Program
{
static void Run(int sampleSize)
{
double[] X = new double[sampleSize];
var r = new Random();
for (int i = 0; i < sampleSize; i++)
X[i] = r.NextDouble();
const int numBuckets = 10;
var histogram = new Histogram(X, numBuckets);
Console.WriteLine("Sample size: {0:N0}", sampleSize);
for (int i = 0; i < numBuckets; i++)
{
string bar = new String('#', (int)(histogram[i].Count * 360 / sampleSize));
Console.WriteLine(" {0:0.00} : {1}", histogram[i].LowerBound, bar);
}
var statistics = new DescriptiveStatistics(X);
Console.WriteLine(" Mean: " + statistics.Mean);
Console.WriteLine("StdDev: " + statistics.StandardDeviation);
Console.WriteLine();
}
static void Main(string[] args)
{
Run(100);
Run(1000);
Run(10000);
}
}</syntaxhighlight>
{{out}}
<pre>Sample size: 100
0.00 : ##################################################
0.10 : ############################
0.20 : ###########################################
0.30 : ############################
0.40 : ###########################################
0.50 : #########################
0.60 : ##############################################
0.70 : #########################
0.80 : #########################
0.90 : ###########################################
Mean: 0.481181871658741
StdDev: 0.301957945953801
Sample size: 1,000
0.00 : ###################################
0.10 : ###################################
0.20 : ############################
0.30 : #################################
0.40 : #######################################
0.50 : #########################################
0.60 : ######################################
0.70 : #################################
0.80 : ##################################
0.90 : ######################################
Mean: 0.508802390412802
StdDev: 0.28593657047378
Sample size: 10,000
0.00 : ##################################
0.10 : #######################################
0.20 : #################################
0.30 : ####################################
0.40 : ###################################
0.50 : #####################################
0.60 : ####################################
0.70 : ###################################
0.80 : ##################################
0.90 : ###################################
Mean: 0.499069400830039
StdDev: 0.287103198996064</pre>
=={{header|C++}}==
<syntaxhighlight lang="cpp">#include <iostream>
#include <random>
#include <vector>
#include <cstdlib>
#include <algorithm>
#include <cmath>
void printStars ( int number ) {
if ( number > 0 ) {
for ( int i = 0 ; i < number + 1 ; i++ )
std::cout << '*' ;
}
std::cout << '\n' ;
}
int main( int argc , char *argv[] ) {
const int numberOfRandoms = std::atoi( argv[1] ) ;
std::random_device rd ;
std::mt19937 gen( rd( ) ) ;
std::uniform_real_distribution<> distri( 0.0 , 1.0 ) ;
std::vector<double> randoms ;
for ( int i = 0 ; i < numberOfRandoms + 1 ; i++ )
randoms.push_back ( distri( gen ) ) ;
std::sort ( randoms.begin( ) , randoms.end( ) ) ;
double start = 0.0 ;
for ( int i = 0 ; i < 9 ; i++ ) {
double to = start + 0.1 ;
int howmany = std::count_if ( randoms.begin( ) , randoms.end( ),
[&start , &to] ( double c ) { return c >= start
&& c < to ; } ) ;
if ( start == 0.0 ) //double 0.0 output as 0
std::cout << "0.0" << " - " << to << ": " ;
else
std::cout << start << " - " << to << ": " ;
if ( howmany > 50 ) //scales big interval numbers to printable length
howmany = howmany / ( howmany / 50 ) ;
printStars ( howmany ) ;
start += 0.1 ;
}
double mean = std::accumulate( randoms.begin( ) , randoms.end( ) , 0.0 ) / randoms.size( ) ;
double sum = 0.0 ;
for ( double num : randoms )
sum += std::pow( num - mean , 2 ) ;
double stddev = std::pow( sum / randoms.size( ) , 0.5 ) ;
std::cout << "The mean is " << mean << " !" << std::endl ;
std::cout << "Standard deviation is " << stddev << " !" << std::endl ;
return 0 ;
}</syntaxhighlight>
{{out}}
<pre>./statistics 100
0.0 - 0.1: **********
0.1 - 0.2: ***************
0.2 - 0.3: **********
0.3 - 0.4: *************
0.4 - 0.5: **********
0.5 - 0.6: *********
0.6 - 0.7: *********
0.7 - 0.8: ************
0.8 - 0.9: *********
The mean is 0.493563 !
Standard deviation is 0.297152 !</pre>
=={{header|CoffeeScript}}==
<syntaxhighlight lang="coffeescript">generate_statistics = (n) ->
hist = {}
update_hist = (r) ->
hist[Math.floor 10*r] ||= 0
hist[Math.floor 10*r] += 1
sum = 0
sum_squares = 0.0
for i in [1..n]
r = Math.random()
sum += r
sum_squares += r*r
update_hist r
mean = sum / n
stddev = Math.sqrt((sum_squares / n) - mean*mean)
[n, mean, stddev, hist]
display_statistics = (n, mean, stddev, hist) ->
console.log "-- Stats for sample size #{n}"
console.log "mean: #{mean}"
console.log "sdev: #{stddev}"
for x, cnt of hist
bars = repeat "=", Math.floor(cnt*300/n)
console.log "#{x/10}: #{bars} #{cnt}"
repeat = (c, n) ->
s = ''
s += c for i in [1..n]
s
for n in [100, 1000, 10000, 1000000]
[n, mean, stddev, hist] = generate_statistics n
display_statistics n, mean, stddev, hist</syntaxhighlight>
{{out}}
<pre>> coffee stats.coffee
-- Stats for sample size 100
mean: 0.5058459933893755
sdev: 0.2752669422150894
0: ================== 6
0.1: ============================================= 15
0.2: =========================== 9
0.3: ===================== 7
0.4: ============================================= 15
0.5: ======================== 8
0.6: ================================= 11
0.7: ========================================== 14
0.8: ===================== 7
0.9: ======================== 8
-- Stats for sample size 1000
mean: 0.49664502244861797
sdev: 0.2942483939245344
0: ========================== 89
0.1: ===================================== 126
0.2: =========================== 93
0.3: ==================================== 121
0.4: =========================== 93
0.5: ====================== 75
0.6: ================================ 108
0.7: ======================== 82
0.8: ============================== 101
0.9: ================================= 112
-- Stats for sample size 10000
mean: 0.4985696110446239
sdev: 0.29007446138438986
0: ============================== 1005
0.1: ============================== 1016
0.2: ============================== 1022
0.3: ============================== 1012
0.4: ============================ 958
0.5: =============================== 1035
0.6: ============================= 974
0.7: ============================= 968
0.8: ============================= 973
0.9: =============================== 1037
-- Stats for sample size 1000000
mean: 0.5001718024678293
sdev: 0.2887130780006248
0: ============================== 100113
0.1: ============================= 99830
0.2: ============================== 100029
0.3: ============================= 99732
0.4: ============================= 99911
0.5: ============================= 99722
0.6: ============================== 100780
0.7: ============================= 99812
0.8: ============================= 99875
0.9: ============================== 100196
</pre>
=={{header|D}}==
{{trans|Python}}
<syntaxhighlight lang="d">import std.stdio, std.algorithm, std.array, std.typecons,
std.range, std.exception;
auto meanStdDev(R)(R numbers) /*nothrow*/ @safe /*@nogc*/ {
if (numbers.empty)
return tuple(0.0L, 0.0L);
real sx = 0.0, sxx = 0.0;
ulong n;
foreach (x; numbers) {
sx += x;
sxx += x ^^ 2;
n++;
}
return tuple(sx / n, (n * sxx - sx ^^ 2) ^^ 0.5L / n);
}
void showHistogram01(R)(R numbers) /*@safe*/ {
enum maxWidth = 50; // N. characters.
ulong[10] bins;
foreach (immutable x; numbers) {
immutable index = cast(size_t)(x * bins.length);
enforce(index >= 0 && index < bins.length);
bins[index]++;
}
immutable real maxFreq = bins.reduce!max;
foreach (immutable n, immutable i; bins)
writefln(" %3.1f: %s", n / real(bins.length),
replicate("*", cast(int)(i / maxFreq * maxWidth)));
writeln;
}
version (statistics_basic_main) {
void main() @safe {
import std.random;
foreach (immutable p; 1 .. 7) {
auto n = iota(10L ^^ p).map!(_ => uniform(0.0L, 1.0L));
writeln(10L ^^ p, " numbers:");
writefln(" Mean: %8.6f, SD: %8.6f", n.meanStdDev.tupleof);
n.showHistogram01;
}
}
}</syntaxhighlight>
Compile with "-version=statistics_basic_main" to run the main function.
{{out}}
<pre>10 numbers:
Mean: 0.651336, SD: 0.220208
0.0: *************************
0.1: **************************************************
0.2:
0.3: **************************************************
0.4:
0.5: *************************
0.6: *************************
0.7: *************************
0.8: *************************
0.9: *************************
100 numbers:
Mean: 0.470756, SD: 0.291080
0.0: *************************************
0.1: *******************************************
0.2: *******************************
0.3: *******************************
0.4: ******************
0.5: *********************
0.6: ****************************
0.7: **************************************************
0.8: *******************************
0.9: ******************
1000 numbers:
Mean: 0.519127, SD: 0.287775
0.0: ***************************************
0.1: *******************************************
0.2: ****************************************
0.3: ****************************************
0.4: ************************************
0.5: ******************************************
0.6: **************************************************
0.7: **************************************
0.8: ********************************************
0.9: **********************************
10000 numbers:
Mean: 0.503266, SD: 0.289198
0.0: **********************************************
0.1: **********************************************
0.2: **************************************************
0.3: ************************************************
0.4: ***********************************************
0.5: *********************************************
0.6: ***********************************************
0.7: ************************************************
0.8: **********************************************
0.9: **********************************************
100000 numbers:
Mean: 0.500945, SD: 0.289076
0.0: *************************************************
0.1: *************************************************
0.2: *************************************************
0.3: *************************************************
0.4: *************************************************
0.5: *************************************************
0.6: *************************************************
0.7: *************************************************
0.8: **************************************************
0.9: *************************************************
1000000 numbers:
Mean: 0.499970, SD: 0.288635
0.0: *************************************************
0.1: *************************************************
0.2: *************************************************
0.3: *************************************************
0.4: *************************************************
0.5: **************************************************
0.6: *************************************************
0.7: *************************************************
0.8: *************************************************
0.9: *************************************************</pre>
=={{header|Dart}}==
<syntaxhighlight lang="d">/* Import math library to get:
* 1) Square root function : Math.sqrt(x)
* 2) Power function : Math.pow(base, exponent)
* 3) Random number generator : Math.Random()
*/
import 'dart:math' as Math show sqrt, pow, Random;
// Returns average/mean of a list of numbers
num mean(List<num> l) => l.reduce((num value,num element)=>value+element)/l.length;
// Returns standard deviation of a list of numbers
num stdev(List<num> l) => Math.sqrt((1/l.length)*l.map((num x)=>x*x).reduce((num value,num element) => value+element) - Math.pow(mean(l),2));
/* CODE TO PRINT THE HISTOGRAM STARTS HERE
*
* Histogram has ten fields, one for every tenth between 0 and 1
* To do this, we save the histogram as a global variable
* that will hold the number of occurences of each tenth in the sample
*/
List<num> histogram = new List.filled(10,0);
/*
* METHOD TO CREATE A RANDOM SAMPLE OF n NUMBERS (Returns a list)
*
* While creating each value, this method also increments the
* appropriate index of the histogram
*/
List<num> randomsample(num n){
List<num> l = new List<num>(n);
histogram = new List.filled(10,0);
num random = new Math.Random();
for (int i = 0; i < n; i++){
l[i] = random.nextDouble();
histogram[conv(l[i])] += 1;
}
return l;
}
/*
* METHOD TO RETURN A STRING OF n ASTERIXES (yay ASCII art)
*/
String stars(num n){
String s = '';
for (int i = 0; i < n; i++){
s = s + '*';
}
return s;
}
/*
* METHOD TO DRAW THE HISTOGRAM
* 1) Get to total for all the values in the histogram
* 2) For every field in the histogram:
* a) Compute the frequency for every field in the histogram
* b) Print the frequency as asterixes
*/
void drawhistogram(){
int total = histogram.reduce((num element,num value)=>element+value);
double freq;
for (int i = 0; i < 10; i++){
freq = histogram[i]/total;
print('${i/10} - ${(i+1)/10} : ' + stars(conv(30*freq)));
}
}
/* HELPER METHOD:
* converts values between 0-1 to integers between 0-9 inclusive
* useful to figure out which random value generated
* corresponds to which field in the histogram
*/
int conv(num i) => (10*i).floor();
/* MAIN FUNCTION
*
* Create 5 histograms and print the mean and standard deviation for each:
* 1) Sample Size = 100
* 2) Sample Size = 1000
* 3) Sample Size = 10000
* 4) Sample Size = 100000
* 5) Sample Size = 1000000
*
*/
void main(){
List<num> l;
num m;
num s;
List<int> sampleSizes = [100,1000,10000,100000,1000000];
for (int samplesize in sampleSizes){
print('--------------- Sample size $samplesize ----------------');
l = randomsample(samplesize);
m = mean(l);
s = stdev(l);
drawhistogram();
print('');
print('mean: ${m.toStringAsPrecision(8)} standard deviation: ${s.toStringAsPrecision(8)}');
print('');
}
}</syntaxhighlight>
{{out}}
<pre>
--------------- Sample size 100 ----------------
0.0 - 0.1 : ******************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : **************************
0.3 - 0.4 : **************************
0.4 - 0.5 : ***************************************
0.5 - 0.6 : *********************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : *********************************
0.8 - 0.9 : ************************
0.9 - 1.0 : **************************
mean: 0.49246975 standard deviation: 0.27789056
--------------- Sample size 1000 ----------------
0.0 - 0.1 : *************************
0.1 - 0.2 : *************************
0.2 - 0.3 : ******************************
0.3 - 0.4 : *******************************
0.4 - 0.5 : *********************************
0.5 - 0.6 : **********************************
0.6 - 0.7 : ********************************
0.7 - 0.8 : ****************************
0.8 - 0.9 : ****************************
0.9 - 1.0 : *******************************
mean: 0.51170283 standard deviation: 0.28170178
-------------- Sample size 10000 ----------------
0.0 - 0.1 : *****************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : ****************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : *****************************
0.5 - 0.6 : ******************************
0.6 - 0.7 : *******************************
0.7 - 0.8 : ******************************
0.8 - 0.9 : ******************************
0.9 - 1.0 : *******************************
mean: 0.50517609 standard deviation: 0.28923152
-------------- Sample size 100000 ----------------
0.0 - 0.1 : ******************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : *****************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : *****************************
0.5 - 0.6 : ******************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : *****************************
0.8 - 0.9 : *****************************
0.9 - 1.0 : ******************************
mean: 0.49994544 standard deviation: 0.28879394
-------------- Sample size 1000000 ----------------
0.0 - 0.1 : *****************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : *****************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : ******************************
0.5 - 0.6 : *****************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : *****************************
0.8 - 0.9 : *****************************
0.9 - 1.0 : ******************************
mean: 0.50013331 standard deviation: 0.28864180
</pre>
=={{header|EasyLang}}==
<syntaxhighlight lang=easylang>
global list[] .
proc mklist n . .
list[] = [ ]
for i = 1 to n
list[] &= randomf
.
.
func mean .
for v in list[]
sum += v
.
return sum / len list[]
.
func stddev .
avg = mean
for v in list[]
squares += (avg - v) * (avg - v)
.
return sqrt (squares / len list[])
.
proc histo . .
len hist[] 10
for v in list[]
ind = floor (v * 10) + 1
hist[ind] += 1
.
for v in hist[]
h = floor (v / len list[] * 200 + 0.5)
s$ = substr "========================================" 1 h
print v & " " & s$
.
.
numfmt 4 5
proc stats size . .
mklist size
print "Size: " & size
print "Mean: " & mean
print "Stddev: " & stddev
histo
print ""
.
stats 100
stats 1000
stats 10000
stats 100000
</syntaxhighlight>
=={{header|Elixir}}==
{{trans|Ruby}}
<syntaxhighlight lang="elixir">defmodule Statistics do
def basic(n) do
{sum, sum2, hist} = generate(n)
mean = sum / n
stddev = :math.sqrt(sum2 / n - mean*mean)
IO.puts "size: #{n}"
IO.puts "mean: #{mean}"
IO.puts "stddev: #{stddev}"
Enum.each(0..9, fn i ->
:io.fwrite "~.1f:~s~n", [0.1*i, String.duplicate("=", trunc(500 * hist[i] / n))]
end)
IO.puts ""
end
defp generate(n) do
hist = for i <- 0..9, into: %{}, do: {i,0}
Enum.reduce(1..n, {0, 0, hist}, fn _,{sum, sum2, h} ->
r = :rand.uniform
{sum+r, sum2+r*r, Map.update!(h, trunc(10*r), &(&1+1))}
end)
end
end
Enum.each([100,1000,10000], fn n ->
Statistics.basic(n)
end)</syntaxhighlight>
{{out}}
<pre>
size: 100
mean: 0.5360891830207845
stddev: 0.2934821336243825
0.0:=======================================================
0.1:=========================
0.2:============================================================
0.3:=============================================
0.4:==============================
0.5:========================================
0.6:===========================================================================
0.7:=======================================================
0.8:=======================================================
0.9:============================================================
size: 1000
mean: 0.4928249370693845
stddev: 0.2877164661860377
0.0:=========================================================
0.1:==============================================
0.2:================================================
0.3:====================================================
0.4:================================================
0.5:======================================================
0.6:================================================
0.7:==================================================
0.8:===================================================
0.9:===========================================
size: 10000
mean: 0.4969580860984137
stddev: 0.289282008094715
0.0:==================================================
0.1:====================================================
0.2:================================================
0.3:=================================================
0.4:================================================
0.5:===================================================
0.6:==================================================
0.7:================================================
0.8:=================================================
0.9:=================================================
</pre>
=={{header|Factor}}==
<syntaxhighlight lang="factor">USING: assocs formatting grouping io kernel literals math
math.functions math.order math.statistics prettyprint random
sequences sequences.deep sequences.repeating ;
IN: rosetta-code.statistics-basic
CONSTANT: granularity
$[ 11 iota [ 10 /f ] map 2 clump ]
: mean/std ( seq -- a b )
[ mean ] [ population-std ] bi ;
: .mean/std ( seq -- )
mean/std [ "Mean: " write . ] [ "STD: " write . ] bi* ;
: count-between ( seq a b -- n )
[ between? ] 2curry count ;
: histo ( seq -- seq )
granularity [ first2 count-between ] with map ;
: bar ( n -- str )
[ dup 50 < ] [ 10 / ] until 2 * >integer "*" swap repeat ;
: (.histo) ( seq -- seq' )
[ bar ] map granularity swap zip flatten 3 group ;
: .histo ( seq -- )
(.histo) [ "%.1f - %.1f %s\n" vprintf ] each ;
: stats ( n -- )
dup "Statistics %d:\n" printf
random-units [ histo .histo ] [ .mean/std nl ] bi ;
: main ( -- )
{ 100 1,000 10,000 } [ stats ] each ;
MAIN: main</syntaxhighlight>
{{out}}
<pre>
Statistics 100:
0.0 - 0.1 ************************
0.1 - 0.2 **************
0.2 - 0.3 **********************
0.3 - 0.4 ********************
0.4 - 0.5 ******
0.5 - 0.6 ****************************
0.6 - 0.7 **********************
0.7 - 0.8 **********************
0.8 - 0.9 ************
0.9 - 1.0 ******************************
Mean: 0.5125865184454739
STD: 0.3011535351273979
Statistics 1000:
0.0 - 0.1 ******************
0.1 - 0.2 **************************
0.2 - 0.3 ********************
0.3 - 0.4 ********************
0.4 - 0.5 ********************
0.5 - 0.6 *********************
0.6 - 0.7 *****************
0.7 - 0.8 ******************
0.8 - 0.9 ******************
0.9 - 1.0 ******************
Mean: 0.4822182628505952
STD: 0.2874411306988986
Statistics 10000:
0.0 - 0.1 *******************
0.1 - 0.2 ********************
0.2 - 0.3 *******************
0.3 - 0.4 *******************
0.4 - 0.5 ********************
0.5 - 0.6 *******************
0.6 - 0.7 *******************
0.7 - 0.8 ********************
0.8 - 0.9 ********************
0.9 - 1.0 ********************
Mean: 0.5030027112958179
STD: 0.2895932850375331
</pre>
=={{header|Fortran}}==
{{works with|Fortran|95 and later}}
This version will handle numbers as large as 1 trillion or more if you are prepared to wait long enough
<syntaxhighlight lang="fortran">program basic_stats
implicit none
integer, parameter :: i64 = selected_int_kind(18)
integer, parameter :: r64 = selected_real_kind(15)
integer(i64), parameter :: samples = 1000000000_i64
real(r64) :: r
real(r64) :: mean, stddev
real(r64) :: sumn = 0, sumnsq = 0
integer(i64) :: n = 0
integer(i64) :: bin(10) = 0
integer :: i, ind
call random_seed
n = 0
do while(n <= samples)
call random_number(r)
ind = r * 10 + 1
bin(ind) = bin(ind) + 1_i64
sumn = sumn + r
sumnsq = sumnsq + r*r
n = n + 1_i64
end do
mean = sumn / n
stddev = sqrt(sumnsq/n - mean*mean)
write(*, "(a, i0)") "sample size = ", samples
write(*, "(a, f17.15)") "Mean : ", mean,
write(*, "(a, f17.15)") "Stddev : ", stddev
do i = 1, 10
write(*, "(f3.1, a, a)") real(i)/10.0, ": ", repeat("=", int(bin(i)*500/samples))
end do
end program</syntaxhighlight>
{{out}}
<pre>sample size = 100
Mean : 0.507952672404959
Stddev : 0.290452178516586
0.1: =============================================
0.2: ============================================================
0.3: ==============================
0.4: =================================================================
0.5: =============================================
0.6: =======================================================
0.7: =================================================================
0.8: ==================================================
0.9: =========================
1.0: =================================================================
sample size = 1000
Mean : 0.505018948813265
Stddev : 0.287904987339785
0.1: ==============================================
0.2: ================================================
0.3: ========================================================
0.4: ===============================================
0.5: ==================================================
0.6: ===========================================
0.7: ========================================================
0.8: ==================================================
0.9: ===================================================
1.0: ===================================================
sample size = 10000
Mean : 0.508929669066967
Stddev : 0.287243609812712
0.1: ==============================================
0.2: ================================================
0.3: =================================================
0.4: ==================================================
0.5: ================================================
0.6: ===================================================
0.7: ==================================================
0.8: ==================================================
0.9: ====================================================
1.0: ===================================================
sample size = 1000000000
Mean : 0.500005969962249
Stddev : 0.288673875345505
0.1: =================================================
0.2: =================================================
0.3: =================================================
0.4: =================================================
0.5: ==================================================
0.6: =================================================
0.7: ==================================================
0.8: =================================================
0.9: ==================================================
1.0: =================================================</pre>
=={{header|Go}}==
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
"math/rand"
"strings"
)
func main() {
sample(100)
sample(1000)
sample(10000)
}
func sample(n int) {
// generate data
d := make([]float64, n)
for i := range d {
d[i] = rand.Float64()
}
// show mean, standard deviation
var sum, ssq float64
for _, s := range d {
sum += s
ssq += s * s
}
fmt.Println(n, "numbers")
m := sum / float64(n)
fmt.Println("Mean: ", m)
fmt.Println("Stddev:", math.Sqrt(ssq/float64(n)-m*m))
// show histogram
h := make([]int, 10)
for _, s := range d {
h[int(s*10)]++
}
for _, c := range h {
fmt.Println(strings.Repeat("*", c*205/int(n)))
}
fmt.Println()
}</syntaxhighlight>
{{out}}
<pre>
100 numbers
Mean: 0.5231064889267764
Stddev: 0.292668237816841
****************
****************
************************
**********************
******************
******************
****************
**************************
************************
********************
1000 numbers
Mean: 0.496026080160094
Stddev: 0.2880988956436907
*********************
********************
*****************
***********************
******************
**********************
********************
*********************
******************
*******************
10000 numbers
Mean: 0.5009091903581223
Stddev: 0.289269693719711
*******************
********************
********************
********************
*********************
********************
*******************
*******************
********************
*********************
</pre>
The usual approach to the extra problem is [http://en.wikipedia.org/wiki/Sampling_%28statistics%29 sampling.] That is, to not do it.
To show really show how computations could be done a trillion numbers however, here is an outline of a map reduce strategy. The main task indicated that numbers should be generated before doing any computations on them. Consistent with that, The function getSegment returns data based on a starting and ending index, as if it were accessing some large data store.
The following runs comfortably on a simulated data size of 10 million. To scale to a trillion, and to use real data, you would want to use a technique like [[Distributed_programming#Go]] to distribute work across multiple computers, and on each computer, use a technique like [[Parallel_calculations#Go]] to distribute work across multiple cores within each computer. You would tune parameters like the constant <tt>threshold</tt> in the code below to optimize cache performance.
<syntaxhighlight lang="go">package main
import (
"fmt"
"math"
"math/rand"
"strings"
)
func main() {
bigSample(1e7)
}
func bigSample(n int64) {
sum, ssq, h := reduce(0, n)
// compute final statistics and output as above
fmt.Println(n, "numbers")
m := sum / float64(n)
fmt.Println("Mean: ", m)
fmt.Println("Stddev:", math.Sqrt(ssq/float64(n)-m*m))
for _, c := range h {
fmt.Println(strings.Repeat("*", c*205/int(n)))
}
fmt.Println()
}
const threshold = 1e6
func reduce(start, end int64) (sum, ssq float64, h []int) {
n := end - start
if n < threshold {
d := getSegment(start, end)
return computeSegment(d)
}
// map to two sub problems
half := (start + end) / 2
sum1, ssq1, h1 := reduce(start, half)
sum2, ssq2, h2 := reduce(half, end)
// combine results
for i, c := range h2 {
h1[i] += c
}
return sum1 + sum2, ssq1 + ssq2, h1
}
func getSegment(start, end int64) []float64 {
d := make([]float64, end-start)
for i := range d {
d[i] = rand.Float64()
}
return d
}
func computeSegment(d []float64) (sum, ssq float64, h []int) {
for _, s := range d {
sum += s
ssq += s * s
}
h = make([]int, 10)
for _, s := range d {
h[int(s*10)]++
}
return
}</syntaxhighlight>
{{out}}
<pre>
10000000 numbers
Mean: 0.4999673191148989
Stddev: 0.2886663876567514
********************
********************
********************
********************
********************
********************
********************
********************
********************
********************
</pre>
=={{header|Haskell}}==
<syntaxhighlight lang="haskell">import Data.Foldable (foldl') --'
import System.Random (randomRs, newStdGen)
import Control.Monad (zipWithM_)
import System.Environment (getArgs)
intervals :: [(Double, Double)]
intervals = map conv [0 .. 9]
where
xs = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
conv s =
let [h, l] = take 2 $ drop s xs
in (h, l)
count :: [Double] -> [Int]
count rands = map (\iv -> foldl'' (loop iv) 0 rands) intervals
where
loop :: (Double, Double) -> Int -> Double -> Int
loop (lo, hi) n x
| lo <= x && x < hi = n + 1
| otherwise = n
-- ^ fuses length and filter within (lo,hi)
data Pair a b =
Pair !a
!b
-- accumulate sum and length in one fold
sumLen :: [Double] -> Pair Double Double
sumLen = fion2 . foldl'' (\(Pair s l) x -> Pair (s + x) (l + 1)) (Pair 0.0 0)
where
fion2 :: Pair Double Int -> Pair Double Double
fion2 (Pair s l) = Pair s (fromIntegral l)
-- safe division on pairs
divl :: Pair Double Double -> Double
divl (Pair _ 0.0) = 0.0
divl (Pair s l) = s / l
-- sumLen and divl are separate for stddev below
mean :: [Double] -> Double
mean = divl . sumLen
stddev :: [Double] -> Double
stddev xs = sqrt $ foldl'' (\s x -> s + (x - m) ^ 2) 0 xs / l
where
p@(Pair s l) = sumLen xs
m = divl p
main = do
nr <- read . head <$> getArgs
-- or in code, e.g. let nr = 1000
rands <- take nr . randomRs (0.0, 1.0) <$> newStdGen
putStrLn $ "The mean is " ++ show (mean rands) ++ " !"
putStrLn $ "The standard deviation is " ++ show (stddev rands) ++ " !"
zipWithM_
(\iv fq -> putStrLn $ ivstr iv ++ ": " ++ fqstr fq)
intervals
(count rands)
where
fqstr i =
replicate
(if i > 50
then div i (div i 50)
else i)
'*'
ivstr (lo, hi) = show lo ++ " - " ++ show hi
-- To avoid Wiki formatting issue
foldl'' = foldl'</syntaxhighlight>
{{out}}
<pre>./Statistics 100
The mean is 0.5007604927009823 !
The standard deviation is 0.2933668702954616 !
0.0 - 0.1: ********
0.1 - 0.2: ************
0.2 - 0.3: ***********
0.3 - 0.4: *************
0.4 - 0.5: *****
0.5 - 0.6: ************
0.6 - 0.7: *********
0.7 - 0.8: ********
0.8 - 0.9: *********
0.9 - 1.0: *************
./Statistics 10000
The mean is 0.49399049116152155 !
The standard deviation is 0.28782134281196275 !
0.0 - 0.1: **************************************************
0.1 - 0.2: **************************************************
0.2 - 0.3: ***************************************************
0.3 - 0.4: **************************************************
0.4 - 0.5: **************************************************
0.5 - 0.6: ***************************************************
0.6 - 0.7: ***************************************************
0.7 - 0.8: ***************************************************
0.8 - 0.9: ****************************************************
0.9 - 1.0: ***************************************************
</pre>
=={{header|Hy}}==
<syntaxhighlight lang="lisp">(import
[numpy.random [random]]
[numpy [mean std]]
[matplotlib.pyplot :as plt])
(for [n [100 1000 10000]]
(setv v (random n))
(print "Mean:" (mean v) "SD:" (std v)))
(plt.hist (random 1000))
(plt.show)</syntaxhighlight>
=={{header|Icon}} and {{header|Unicon}}==
The following uses the ''stddev'' procedure from the [[Standard_deviation]] task.
In this example,
<syntaxhighlight lang="icon">procedure main(A)
W := 50 # avg width for histogram bar
B := 10 # histogram bins
if *A = 0 then put(A,100) # 100 if none specified
while N := get(A) do { # once per argument
write("\nN=",N)
N := 0 < integer(N) | next # skip if invalid
stddev() # reset
m := 0.
H := list(B,0) # Histogram of
every i := 1 to N do { # calc running ...
s := stddev(r := ?0) # ... std dev
m +:= r/N # ... mean
H[integer(*H*r)+1] +:= 1 # ... histogram
}
write("mean=",m)
write("stddev=",s)
every i := 1 to *H do # show histogram
write(right(real(i)/*H,5)," : ",repl("*",integer(*H*50./N*H[i])))
}
end</syntaxhighlight>
{{out}}
<pre>
N=100
mean=0.4941076275054806
stddev=0.2812938788216594
0.1 : ****************************************
0.2 : *******************************************************
0.3 : *******************************************************
0.4 : **********************************************************************
0.5 : ****************************************
0.6 : *********************************************
0.7 : ****************************************
0.8 : *****************************************************************
0.9 : ****************************************
1.0 : **************************************************
N=10000
mean=0.4935428224375008
stddev=0.2884171825227816
0.1 : ***************************************************
0.2 : ***************************************************
0.3 : ***************************************************
0.4 : **************************************************
0.5 : ****************************************************
0.6 : *************************************************
0.7 : ***********************************************
0.8 : ************************************************
0.9 : **************************************************
1.0 : ***********************************************
N=1000000
mean=0.4997503773607869
stddev=0.2886322440610256
0.1 : *************************************************
0.2 : **************************************************
0.3 : **************************************************
0.4 : **************************************************
0.5 : *************************************************
0.6 : **************************************************
0.7 : *************************************************
0.8 : *************************************************
0.9 : **************************************************
1.0 : *************************************************</pre>
=={{header|J}}==
J has library routines to compute mean and standard deviation:
<
(mean,stddev)
0.484669 0.287482
(mean,stddev)
0.503642 0.290777
(mean,stddev)
0.499677 0.288726</syntaxhighlight>
And, for a histogram:
<syntaxhighlight lang="j">histogram=: <: @ (#/.~) @ (i.@#@[ , I.)
require'plot'
plot ((% * 1 + i.)100) ([;histogram) 10000 ?@$ 0</syntaxhighlight>
but these are not quite what is being asked for here.
Instead:
<syntaxhighlight lang="j">histogram=: <: @ (#/.~) @ (i.@#@[ , I.)
meanstddevP=: 3 :0
NB. compute mean and std dev of y random numbers
NB. picked from even distribution between 0 and 1
NB. and display a normalized ascii histogram for this sample
NB. note: uses population mean (0.5), not sample mean, for stddev
NB. given the equation specified for this task.
h=.s=.t=. 0
chunk=. 1e6
bins=. (%~ 1 + i.) 10
for. i. <.y%chunk do.
data=. chunk ?@$ 0
h=. h+ bins histogram data
s=. s+ +/ data
t=. t+ +/ *: data-0.5
end.
h=. h+ bins histogram data
s=. s+ +/ data
t=. t+ +/ *: data - 0.5
smoutput (<.300*h%y) #"0 '#'
(s%y) , %:t%y
)</syntaxhighlight>
Example use:
<
#############################
####################################
###########################
##############################
###################################
########################
###########################
############################
################################
##########################
0.488441 0.289744
meanstddevP 10000
##############################
##############################
#############################
#############################
###############################
##############################
############################
##############################
#############################
#############################
0.49697 0.289433
meanstddevP 100000
#############################
##############################
#############################
#############################
#############################
##############################
##############################
##############################
##############################
#############################
0.500872 0.288241</syntaxhighlight>
(That said, note that these numbers are random, so reported standard deviation will vary with the random sample being tested.)
This could handle a trillion random numbers on a bog-standard computer, but I am not inclined to wait that long.
=={{header|Java}}==
Translation of [[Statistics/Basic#Python|Python]] via [[Statistics/Basic#D|D]]
{{works with|Java|8}}
<syntaxhighlight lang="java">import static java.lang.Math.pow;
import static java.util.Arrays.stream;
import static java.util.stream.Collectors.joining;
import static java.util.stream.IntStream.range;
public class Test {
static double[] meanStdDev(double[] numbers) {
if (numbers.length == 0)
return new double[]{0.0, 0.0};
double sx = 0.0, sxx = 0.0;
long n = 0;
for (double x : numbers) {
sx += x;
sxx += pow(x, 2);
n++;
}
return new double[]{sx / n, pow((n * sxx - pow(sx, 2)), 0.5) / n};
}
static String replicate(int n, String s) {
return range(0, n + 1).mapToObj(i -> s).collect(joining());
}
static void showHistogram01(double[] numbers) {
final int maxWidth = 50;
long[] bins = new long[10];
for (double x : numbers)
bins[(int) (x * bins.length)]++;
double maxFreq = stream(bins).max().getAsLong();
for (int i = 0; i < bins.length; i++)
System.out.printf(" %3.1f: %s%n", i / (double) bins.length,
replicate((int) (bins[i] / maxFreq * maxWidth), "*"));
System.out.println();
}
public static void main(String[] a) {
Locale.setDefault(Locale.US);
for (int p = 1; p < 7; p++) {
double[] n = range(0, (int) pow(10, p))
.mapToDouble(i -> Math.random()).toArray();
System.out.println((int)pow(10, p) + " numbers:");
double[] res = meanStdDev(n);
System.out.printf(" Mean: %8.6f, SD: %8.6f%n", res[0], res[1]);
showHistogram01(n);
}
}
}</syntaxhighlight>
<pre>10 numbers:
Mean: 0.564409, SD: 0.249601
0.0: *
0.1: *****************
0.2: *****************
0.3: *****************
0.4: *****************
0.5: *****************
0.6: *
0.7: ***************************************************
0.8: **********************************
0.9: *
100 numbers:
Mean: 0.487440, SD: 0.283866
0.0: ************************************
0.1: ************************************
0.2: **********************
0.3: ***************************************************
0.4: ***************************************************
0.5: *****************************
0.6: ************************************
0.7: ************************************
0.8: ************************************
0.9: *****************************
1000 numbers:
Mean: 0.500521, SD: 0.285790
0.0: **********************************************
0.1: ********************************************
0.2: ******************************************
0.3: ****************************************
0.4: **************************************************
0.5: ***************************************************
0.6: ************************************************
0.7: ************************************************
0.8: ****************************************
0.9: *******************************************
10000 numbers:
Mean: 0.499363, SD: 0.288427
0.0: *************************************************
0.1: *************************************************
0.2: ************************************************
0.3: *************************************************
0.4: ***************************************************
0.5: ************************************************
0.6: ***************************************************
0.7: ************************************************
0.8: ************************************************
0.9: ************************************************
100000 numbers:
Mean: 0.500154, SD: 0.287981
0.0: *************************************************
0.1: **************************************************
0.2: **************************************************
0.3: **************************************************
0.4: **************************************************
0.5: ***************************************************
0.6: **************************************************
0.7: **************************************************
0.8: *************************************************
0.9: **************************************************
1000000 numbers:
Mean: 0.500189, SD: 0.288560
0.0: **************************************************
0.1: **************************************************
0.2: **************************************************
0.3: ***************************************************
0.4: **************************************************
0.5: **************************************************
0.6: **************************************************
0.7: **************************************************
0.8: **************************************************
0.9: **************************************************</pre>
=={{header|jq}}==
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
The following jq program uses a streaming approach so that only one PRN (pseudo-random number)
need be in memory at a time.
For PRNs in [0,1], as here, the program is thus essentially only limited by available CPU time.
In the example section below, we include N=100 million.
Since jq does not currently have a built-in PRNG, we will use an external source
of entropy; there are, however, RC entries giving PRN generators written in jq that could be used,
e.g. https://rosettacode.org/wiki/Subtractive_generator#jq
For the sake of illustration, we will use /dev/urandom encapsulated in a shell function:
<syntaxhighlight lang="sh"># Usage: prng N width
function prng {
cat /dev/urandom | tr -cd '0-9' | fold -w "$2" | head -n "$1"
}</syntaxhighlight>
'''basicStats.jq'''
<syntaxhighlight lang="jq"> # $histogram should be a JSON object, with buckets as keys and frequencies as values;
# $keys should be an array of all the potential bucket names (possibly integers)
# in the order to be used for display:
def pp($histogram; $keys):
([$histogram[]] | add) as $n # for scaling
| ($keys|length) as $length
| $keys[]
| "\(.) : \("*" * (($histogram[tostring] // 0) * 20 * $length / $n) // "" )" ;
# `basic_stats` computes the unadjusted standard deviation
# and assumes the sum of squares (ss) can be computed without concern for overflow.
# The histogram is based on allocation to a bucket, which is made
# using `bucketize`, e.g. `.*10|floor`
def basic_stats(stream; bucketize):
# Use
reduce stream as $x ({histogram: {}};
.count += 1
| .sum += $x
| .ss += $x * $x
| ($x | bucketize | tostring) as $bucket
| .histogram[$bucket] += 1 )
| .mean = (.sum / .count)
| .stddev = (((.ss/.count) - .mean*.mean) | sqrt) ;
basic_stats( "0." + inputs | tonumber; .*10|floor)
| "
Basic statistics for \(.count) PRNs in [0,1]:
mean: \(.mean)
stddev: \(.stddev)
Histogram dividing [0,1] into 10 equal intervals:",
pp(.histogram; [range(0;10)] )</syntaxhighlight>
'''Driver Script''' (e.g. bash)
<syntaxhighlight lang="text">for n in 100 1000 1000000 100000000; do
echo "Basic statistics for $n PRNs in [0,1]"
prng $n 10 | jq -nrR -f basicStats.jq
echo
done</syntaxhighlight>
{{out}}
<pre>
Basic statistics for 100 PRNs in [0,1]:
mean: 0.4751625517819999
stddev: 0.2875486981539608
Histogram dividing [0,1] into 10 equal intervals:
0 : **********************
1 : ****************************
2 : ******************
3 : ********************
4 : **************
5 : **********************
6 : **********************
7 : ********************
8 : ******************
9 : ****************
Basic statistics for 1000 PRNs in [0,1]:
mean: 0.4943404721135997
stddev: 0.2912864574615721
Histogram dividing [0,1] into 10 equal intervals:
0 : *********************
1 : ********************
2 : ********************
3 : ******************
4 : ********************
5 : ******************
6 : *********************
7 : ********************
8 : ****************
9 : *********************
Basic statistics for 1000000 PRNs in [0,1]:
mean: 0.5000040604203146
stddev: 0.28858826757261763
Histogram dividing [0,1] into 10 equal intervals:
0 : *******************
1 : *******************
2 : ********************
3 : ********************
4 : ********************
5 : ********************
6 : ********************
7 : *******************
8 : ********************
9 : *******************
Basic statistics for 100000000 PRNs in [0,1]:
mean: 0.4999478413866642
stddev: 0.2886986905535449
Histogram dividing [0,1] into 10 equal intervals:
0 : ********************
1 : ********************
2 : ********************
3 : *******************
4 : ********************
5 : *******************
6 : *******************
7 : *******************
8 : ********************
9 : ********************
</pre>
=={{header|Jsish}}==
<syntaxhighlight lang="javascript">#!/usr/bin/env jsish
"use strict";
function statisticsBasic(args:array|string=void, conf:object=void) {
var options = { // Rosetta Code, Statistics/Basic
rootdir :'', // Root directory.
samples : 0 // Set sample size from options
};
var self = { };
parseOpts(self, options, conf);
function generateStats(n:number):object {
var i, sum = 0, sum2 = 0;
var hist = new Array(10);
hist.fill(0);
for (i = 0; i < n; i++) {
var r = Math.random();
sum += r;
sum2 += r*r;
hist[Math.floor((r*10))] += 1;
}
var mean = sum/n;
var stddev = Math.sqrt((sum2 / n) - mean*mean);
var obj = {n:n, sum:sum, mean:mean, stddev:stddev};
return {n:n, sum:sum, mean:mean, stddev:stddev, hist:hist};
}
function reportStats(summary:object):void {
printf("Samples: %d, mean: %f, stddev: %f\n", summary.n, summary.mean, summary.stddev);
var max = Math.max.apply(summary, summary.hist);
for (var i = 0; i < 10; i++) {
printf("%3.1f+ %-70s %5d\n", i * 0.1, 'X'.repeat(70 * summary.hist[i] / max), summary.hist[i]);
}
return;
}
function main() {
LogTest('Starting', args);
switch (typeof(args)) {
case 'string': args = [args]; break;
case 'array': break;
default: args = [];
}
if (self.rootdir === '')
self.rootdir=Info.scriptDir();
Math.srand(0);
if (self.samples > 0) reportStats(generateStats(self.samples));
else if (args[0] && parseInt(args[0])) reportStats(generateStats(parseInt(args[0])));
else for (var n of [100, 1000, 10000]) reportStats(generateStats(n));
debugger;
LogDebug('Done');
return 0;
}
return main();
}
provide(statisticsBasic, 1);
if (isMain()) {
if (!Interp.conf('unitTest'))
return runModule(statisticsBasic);
;' statisticsBasic unit-test';
; statisticsBasic();
}
/*
=!EXPECTSTART!=
' statisticsBasic unit-test'
statisticsBasic() ==> Samples: 100, mean: 0.534517, stddev: 0.287124
0.0+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 8
0.1+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 11
0.2+ XXXXXXXXXXXXXXXXXXXXXXXXXX 6
0.3+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 10
0.4+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 10
0.5+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 11
0.6+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 8
0.7+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 16
0.8+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 7
0.9+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 13
Samples: 1000, mean: 0.490335, stddev: 0.286562
0.0+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 98
0.1+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 122
0.2+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 85
0.3+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 106
0.4+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 105
0.5+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 101
0.6+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 93
0.7+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 106
0.8+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 98
0.9+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 86
Samples: 10000, mean: 0.499492, stddev: 0.287689
0.0+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 969
0.1+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 992
0.2+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1067
0.3+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1011
0.4+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 973
0.5+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 1031
0.6+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 971
0.7+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 999
0.8+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 991
0.9+ XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX 996
0
=!EXPECTEND!=
*/</syntaxhighlight>
{{out}}
<pre>prompt$ jsish -u statisticsBasic.jsi
[PASS] statisticsBasic.jsi</pre>
=={{header|Julia}}==
<syntaxhighlight lang="julia">using Printf
function hist(numbers)
maxwidth = 50
h = fill(0, 10)
for n in numbers
h[ceil(Int, 10n)] += 1
end
mx = maximum(h)
for (n, i) in enumerate(h)
@printf("%3.1f: %s\n", n / 10, "+" ^ floor(Int, i / mx * maxwidth))
end
end
for i in 1:6
n = rand(10 ^ i)
println("\n##\n## $(10 ^ i) numbers")
@printf("μ: %8.6f; σ: %8.6f\n", mean(n), std(n))
hist(n)
end</syntaxhighlight>
{{out}}
<pre>
##
## 10 numbers
μ: 0.513345; σ: 0.261532
0.1:
0.2: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.3:
0.4: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.6:
0.7: +++++++++++++++++++++++++
0.8: +++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++++++++++++
1.0:
##
## 100 numbers
μ: 0.483039; σ: 0.289858
0.1: ++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++
0.7: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.8: +++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++++++++
1.0: ++++++++++++++++++++++++++++++++++
##
## 1000 numbers
μ: 0.482115; σ: 0.288932
0.1: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++
1.0: +++++++++++++++++++++++++++++++++++
##
## 10000 numbers
μ: 0.502500; σ: 0.288759
0.1: ++++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++++++++
0.4: +++++++++++++++++++++++++++++++++++++++++++++++++
0.5: +++++++++++++++++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++++++++++
1.0: +++++++++++++++++++++++++++++++++++++++++++++++++
##
## 100000 numbers
μ: 0.499489; σ: 0.288911
0.1: +++++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++++++++++++++++
0.6: +++++++++++++++++++++++++++++++++++++++++++++++++
0.7: ++++++++++++++++++++++++++++++++++++++++++++++++
0.8: +++++++++++++++++++++++++++++++++++++++++++++++++
0.9: +++++++++++++++++++++++++++++++++++++++++++++++++
1.0: ++++++++++++++++++++++++++++++++++++++++++++++++
##
## 1000000 numbers
μ: 0.500268; σ: 0.288622
0.1: +++++++++++++++++++++++++++++++++++++++++++++++++
0.2: +++++++++++++++++++++++++++++++++++++++++++++++++
0.3: +++++++++++++++++++++++++++++++++++++++++++++++++
0.4: +++++++++++++++++++++++++++++++++++++++++++++++++
0.5: +++++++++++++++++++++++++++++++++++++++++++++++++
0.6: +++++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.9: +++++++++++++++++++++++++++++++++++++++++++++++++
1.0: +++++++++++++++++++++++++++++++++++++++++++++++++</pre>
=={{header|Klong}}==
Using the "mu" (mean) and "sd" (standard deviation) functions from the
Klong statistics library:
<syntaxhighlight lang="k">
.l("nstat.kg")
bar::{x{x;.d("*")}:*0;.p("")}
hist10::{[s];#'=s@<s::_x*10}
plot::{[s];.p("");.p("n = ",$x);
(!10){.d(x%10);.d(" ");bar(y)}'_(100%x)*(hist10(s::{x;.rn()}'!x));
.p("mean = ",$mu(s));.p("sd = ",$sd(s))}
plot(100)
plot(1000)
plot(10000)
</syntaxhighlight>
{{out}}
<pre>
n = 100
0.0 *****************
0.1 ******
0.2 ********
0.3 **********
0.4 ***********
0.5 *********
0.6 ***********
0.7 **********
0.8 ******
0.9 ************
mean = 0.482634518758
sd = 0.300804579739938409
n = 1000
0.0 *******
0.1 ********
0.2 ***********
0.3 ***********
0.4 *********
0.5 ***********
0.6 ********
0.7 ************
0.8 **********
0.9 ********
mean = 0.510119356421
sd = 0.277396945925369919
n = 10000
0.0 **********
0.1 *********
0.2 *********
0.3 **********
0.4 *********
0.5 **********
0.6 *********
0.7 *********
0.8 **********
0.9 **********
mean = 0.49854591894824
sd = 0.290375399458904972
</pre>
=={{header|Kotlin}}==
{{trans|FreeBASIC}}
<syntaxhighlight lang="scala">// version 1.1.2
val rand = java.util.Random()
fun basicStats(sampleSize: Int) {
if (sampleSize < 1) return
val r = DoubleArray(sampleSize)
val h = IntArray(10) // all zero by default
/*
Generate 'sampleSize' random numbers in the interval [0, 1)
and calculate in which box they will fall when drawing the histogram
*/
for (i in 0 until sampleSize) {
r[i] = rand.nextDouble()
h[(r[i] * 10).toInt()]++
}
// adjust one of the h[] values if necessary to ensure they sum to sampleSize
val adj = sampleSize - h.sum()
if (adj != 0) {
for (i in 0..9) {
h[i] += adj
if (h[i] >= 0) break
h[i] -= adj
}
}
val mean = r.average()
val sd = Math.sqrt(r.map { (it - mean) * (it - mean) }.average())
// Draw a histogram of the data with interval 0.1
var numStars: Int
// If sample size > 500 then normalize histogram to 500
val scale = if (sampleSize <= 500) 1.0 else 500.0 / sampleSize
println("Sample size $sampleSize\n")
println(" Mean ${"%1.6f".format(mean)} SD ${"%1.6f".format(sd)}\n")
for (i in 0..9) {
print(" %1.2f : ".format(i / 10.0))
print("%5d ".format(h[i]))
numStars = (h[i] * scale + 0.5).toInt()
println("*".repeat(numStars))
}
println()
}
fun main(args: Array<String>) {
val sampleSizes = intArrayOf(100, 1_000, 10_000, 100_000)
for (sampleSize in sampleSizes) basicStats(sampleSize)
}</syntaxhighlight>
Sample run:
{{out}}
<pre>
Sample size 100
Mean 0.489679 SD 0.286151
0.00 : 12 ************
0.10 : 7 *******
0.20 : 13 *************
0.30 : 9 *********
0.40 : 10 **********
0.50 : 8 ********
0.60 : 14 **************
0.70 : 10 **********
0.80 : 8 ********
0.90 : 9 *********
Sample size 1000
Mean 0.497003 SD 0.290002
0.00 : 104 ****************************************************
0.10 : 92 **********************************************
0.20 : 107 ******************************************************
0.30 : 109 *******************************************************
0.40 : 96 ************************************************
0.50 : 111 ********************************************************
0.60 : 87 ********************************************
0.70 : 79 ****************************************
0.80 : 117 ***********************************************************
0.90 : 98 *************************************************
Sample size 10000
Mean 0.505243 SD 0.288944
0.00 : 991 **************************************************
0.10 : 938 ***********************************************
0.20 : 1034 ****************************************************
0.30 : 958 ************************************************
0.40 : 963 ************************************************
0.50 : 1003 **************************************************
0.60 : 1081 ******************************************************
0.70 : 995 **************************************************
0.80 : 1001 **************************************************
0.90 : 1036 ****************************************************
Sample size 100000
Mean 0.500501 SD 0.288766
0.00 : 10015 **************************************************
0.10 : 9844 *************************************************
0.20 : 10012 **************************************************
0.30 : 10160 ***************************************************
0.40 : 10051 **************************************************
0.50 : 9938 **************************************************
0.60 : 9934 **************************************************
0.70 : 9914 **************************************************
0.80 : 10057 **************************************************
0.90 : 10075 **************************************************
</pre>
=={{header|Lasso}}==
<syntaxhighlight lang="lasso">define stat1(a) => {
if(#a->size) => {
local(mean = (with n in #a sum #n) / #a->size)
local(sdev = math_pow(((with n in #a sum Math_Pow((#n - #mean),2)) / #a->size),0.5))
return (:#sdev, #mean)
else
return (:0,0)
}
}
define stat2(a) => {
if(#a->size) => {
local(sx = 0, sxx = 0)
with x in #a do => {
#sx += #x
#sxx += #x*#x
}
local(sdev = math_pow((#a->size * #sxx - #sx * #sx),0.5) / #a->size)
return (:#sdev, #sx / #a->size)
else
return (:0,0)
}
}
define histogram(a) => {
local(
out = '\r',
h = array(0,0,0,0,0,0,0,0,0,0,0),
maxwidth = 50,
sc = 0
)
with n in #a do => {
#h->get(integer(#n*10)+1) += 1
}
local(mx = decimal(with n in #h max #n))
with i in #h do => {
#out->append((#sc/10.0)->asString(-precision=1)+': '+('+' * integer(#i / #mx * #maxwidth))+'\r')
#sc++
}
return #out
}
with scale in array(100,1000,10000,100000) do => {^
local(n = array)
loop(#scale) => { #n->insert(decimal_random) }
local(sdev1,mean1) = stat1(#n)
local(sdev2,mean2) = stat2(#n)
#scale' numbers:\r'
'Naive method: sd: '+#sdev1+', mean: '+#mean1+'\r'
'Second method: sd: '+#sdev2+', mean: '+#mean2+'\r'
histogram(#n)
'\r\r'
^}</syntaxhighlight>
{{out}}
<pre>100 numbers:
Naive method: sd: 0.291640, mean: 0.549633
Second method: sd: 0.291640, mean: 0.549633
0.0: ++++++++++++++++++
0.1: ++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++
0.3: +++++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++++
0.5: +++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.9: +++++++++++++++++++++++++++++++++++++++++++
1.0: +++++++++++++++++++++++++++++
1000 numbers:
Naive method: sd: 0.288696, mean: 0.500533
Second method: sd: 0.288696, mean: 0.500533
0.0: +++++++++++++++++++++
0.1: +++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++
0.3: +++++++++++++++++++++++++++++++
0.4: +++++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++++++++
0.7: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++
1.0: +++++++++++++++++++
10000 numbers:
Naive method: sd: 0.289180, mean: 0.496726
Second method: sd: 0.289180, mean: 0.496726
0.0: ++++++++++++++++++++++++
0.1: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.4: +++++++++++++++++++++++++++++++++++++++++++++++
0.5: +++++++++++++++++++++++++++++++++++++++++++++++
0.6: +++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++++++++++++++
0.9: +++++++++++++++++++++++++++++++++++++++++++++++
1.0: +++++++++++++++++++++++
100000 numbers:
Naive method: sd: 0.288785, mean: 0.500985
Second method: sd: 0.288785, mean: 0.500985
0.0: +++++++++++++++++++++++++
0.1: +++++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++++++++
0.3: +++++++++++++++++++++++++++++++++++++++++++++++++
0.4: +++++++++++++++++++++++++++++++++++++++++++++++++
0.5: +++++++++++++++++++++++++++++++++++++++++++++++++
0.6: +++++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++++++++++++
1.0: ++++++++++++++++++++++++</pre>
=={{header|Lua}}==
The standard deviation seems to converge to around 0.28. I expect there's a good reason for this, though it's entirely beyond me.
<syntaxhighlight lang="lua">
math.randomseed(os.time())
function randList (n) -- Build table of size n
local numbers = {}
for i = 1, n do
table.insert(numbers, math.random()) -- range correct by default
end
return numbers
end
function mean (t) -- Find mean average of values in table t
local sum = 0
for k, v in pairs(t) do
sum = sum + v
end
return sum / #t
end
function stdDev (t) -- Find population standard deviation of table t
local squares, avg = 0, mean(t)
for k, v in pairs(t) do
squares = squares + ((avg - v) ^ 2)
end
local variance = squares / #t
return math.sqrt(variance)
end
function showHistogram (t) -- Draw histogram of given table to stdout
local histBars, compVal = {}
for range = 0, 9 do
histBars[range] = 0
for k, v in pairs(t) do
compVal = tonumber(string.format("%0.1f", v - 0.05))
if compVal == range / 10 then
histBars[range] = histBars[range] + 1
end
end
end
for k, v in pairs(histBars) do
io.write("0." .. k .. " " .. string.rep('=', v / #t * 200))
print(" " .. v)
end
print()
end
function showStats (tabSize) -- Create and display statistics info
local numList = randList(tabSize)
print("Table of size " .. #numList)
print("Mean average: " .. mean(numList))
print("Standard dev: " .. stdDev(numList))
showHistogram(numList)
end
for power = 2, 5 do -- Start of main procedure
showStats(10 ^ power)
end
</syntaxhighlight>
=={{header|Maple}}==
The following samples 100 uniformly distributed numbers between 0 and 1:
<syntaxhighlight lang="maple">with(Statistics):
X_100 := Sample( Uniform(0,1), 100 );
Mean( X_100 );
StandardDeviation( X_100 );
Histogram( X_100 );</syntaxhighlight>
It is also possible to make a procedure that outputs the mean, standard deviation, and a histogram for a given number of random uniformly distributed numbers:
<syntaxhighlight lang="maple">sample := proc( n )
local data;
data := Sample( Uniform(0,1), n );
printf( "Mean: %.4f\nStandard Deviation: %.4f",
Statistics:-Mean( data ),
Statistics:-StandardDeviation( data ) );
return Statistics:-Histogram( data );
end proc:
sample( 1000 );</syntaxhighlight>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">Sample[n_]:= (Print[#//Length," numbers, Mean : ",#//Mean,", StandardDeviation : ",#//StandardDeviation ];
BarChart[BinCounts[#,{0,1,.1}], Axes->False, BarOrigin->Left])&[(RandomReal[1,#])&[ n ]]
Sample/@{100,1 000,10 000,1 000 000} </syntaxhighlight>
{{out}}
<pre>100 numbers, Mean : 0.478899, StandardDeviation : 0.322265
1000 numbers, Mean : 0.503383, StandardDeviation : 0.278352
10000 numbers, Mean : 0.498278, StandardDeviation : 0.28925
1000000 numbers, Mean : 0.500248, StandardDeviation : 0.288713</pre>
[[File:mma_basicstat.PNG]]
=={{header|MATLAB}} / {{header|Octave}}==
<syntaxhighlight lang="matlab"> % Initialize
N = 0; S=0; S2 = 0;
binlist = 0:.1:1;
h = zeros(1,length(binlist)); % initialize histogram
% read data and perform computation
while (1)
% read next sample x
if (no_data_available) break; end;
N = N + 1;
S = S + x;
S2= S2+ x*x;
ix= sum(x < binlist);
h(ix) = h(ix)+1;
end
% generate output
m = S/N; % mean
sd = sqrt(S2/N-mean*mean); % standard deviation
bar(binlist,h)</syntaxhighlight>
=={{header|MiniScript}}==
A little Stats class is defined that can calculate mean and standard deviation for a stream of numbers (of arbitrary size, so yes, this would work for a trillion numbers just as well as for one).
<syntaxhighlight lang="miniscript">Stats = {}
Stats.count = 0
Stats.sum = 0
Stats.sumOfSquares = 0
Stats.histo = null
Stats.add = function(x)
self.count = self.count + 1
self.sum = self.sum + x
self.sumOfSquares = self.sumOfSquares + x*x
bin = floor(x*10)
if not self.histo then self.histo = [0]*10
self.histo[bin] = self.histo[bin] + 1
end function
Stats.mean = function()
return self.sum / self.count
end function
Stats.stddev = function()
m = self.sum / self.count
return sqrt(self.sumOfSquares / self.count - m*m)
end function
Stats.histogram = function()
for i in self.histo.indexes
print "0." + i + ": " + "=" * (self.histo[i]/self.count * 200)
end for
end function
for sampleSize in [100, 1000, 10000]
print "Samples: " + sampleSize
st = new Stats
for i in range(sampleSize)
st.add rnd
end for
print "Mean: " + st.mean + " Standard Deviation: " + st.stddev
st.histogram
end for</syntaxhighlight>
{{out}}
<pre>Samples: 100
Mean: 0.484705 Standard Deviation: 0.276974
0.0: ===================
0.1: =======================
0.2: =================
0.3: =================
0.4: =====================
0.5: ===================
0.6: =========================
0.7: =================
0.8: =====================
0.9: =============
Samples: 1000
Mean: 0.509347 Standard Deviation: 0.298134
0.0: ======================
0.1: =================
0.2: ====================
0.3: =====================
0.4: ===============
0.5: ==================
0.6: =================
0.7: ====================
0.8: =======================
0.9: =====================
Samples: 10000
Mean: 0.499573 Standard Deviation: 0.288983
0.0: ===================
0.1: ====================
0.2: ====================
0.3: ====================
0.4: ===================
0.5: ===================
0.6: ====================
0.7: ====================
0.8: ===================
0.9: ===================</pre>
=={{header|Nim}}==
The standard module “stats” provides procedures to compute the statistical moments. It is possible to compute them either on a list of values or incrementally using an object <code>RunningStat</code>. In the following program, we use the first method for the 100 numbers samples and we draw the histogram. For the 1_000, 10_000, 100_000 and 1_000_000 samples, we use the second method which avoids to store the values (but don’t draw the histogram).
<syntaxhighlight lang="nim">import random, sequtils, stats, strutils, strformat
proc drawHistogram(ns: seq[float]) =
var h = newSeq[int](11)
for n in ns:
let pos = (n * 10).toInt
inc h[pos]
const maxWidth = 50
let mx = max(h)
echo ""
for n, count in h:
echo n.toFloat / 10, ": ", repeat('+', int(count / mx * maxWidth))
echo ""
randomize()
# First part: compute directly from a sequence of values.
echo "For 100 numbers:"
let ns = newSeqWith(100, rand(1.0))
echo &"μ = {ns.mean:.12f} σ = {ns.standardDeviation:.12f}"
ns.drawHistogram()
# Second part: compute incrementally using "RunningStat".
for count in [1_000, 10_000, 100_000, 1_000_000]:
echo &"For {count} numbers:"
var rs: RunningStat
for _ in 1..count:
let n = rand(1.0)
rs.push(n)
echo &"μ = {rs.mean:.12f} σ = {rs.standardDeviation:.12f}"
echo()</syntaxhighlight>
{{out}}
<pre>For 100 numbers:
μ = 0.481116458247 σ = 0.282937480658
0.0: +++++++++++++++++
0.1: ++++++++++++++++++++++++++
0.2: ++++++++++++++++++++
0.3: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.4: +++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++
0.6: ++++++++++++++
0.7: +++++++++++++++++++++++++++++
0.8: ++++++++++++++++++++++++++++++++
0.9: +++++++++++++++++++++++
1.0: +++++++++++
For 1000 numbers:
μ = 0.502885271083 σ = 0.293185154479
For 10000 numbers:
μ = 0.496057426121 σ = 0.290222037633
For 100000 numbers:
μ = 0.500358171646 σ = 0.287736290437
For 1000000 numbers:
μ = 0.499972729013 σ = 0.288699343364</pre>
=={{header|Oforth}}==
<syntaxhighlight lang="oforth">: main(n)
| l m std i nb |
// Create list and calculate avg and stddev
ListBuffer init(n, #[ Float rand ]) dup ->l avg ->m
0 l apply(#[ sq +]) n / m sq - sqrt ->std
System.Out "n = " << n << ", avg = " << m << ", std = " << std << cr
// Histo
0.0 0.9 0.1 step: i [
l count(#[ between(i, i 0.1 +) ]) 400 * n / asInteger ->nb
System.Out i <<wjp(3, JUSTIFY_RIGHT, 2) " - " <<
i 0.1 + <<wjp(3, JUSTIFY_RIGHT, 2) " - " <<
StringBuffer new "*" <<n(nb) << cr
] ;</syntaxhighlight>
{{out}}
<pre>
>100 main
n = 100, avg = 0.483425493606762, std = 0.280986417046947
0 - 0.1 - ********************************
0.1 - 0.2 - ****************************************************
0.2 - 0.3 - ************************************************
0.3 - 0.4 - ************************************
0.4 - 0.5 - ********************************
0.5 - 0.6 - ****************************************************
0.6 - 0.7 - ********************************
0.7 - 0.8 - ****************************************************
0.8 - 0.9 - ****************************************
0.9 - 1 - ************************
ok
>main(1000)
n = 1000, avg = 0.514985138392994, std = 0.288119541786792
0 - 0.1 - ************************************
0.1 - 0.2 - **************************************
0.2 - 0.3 - ********************************
0.3 - 0.4 - ***********************************************
0.4 - 0.5 - ************************************
0.5 - 0.6 - ***************************************
0.6 - 0.7 - ***************************************
0.7 - 0.8 - ****************************************
0.8 - 0.9 - *******************************************
0.9 - 1 - *********************************************
ok
>main(10000)
n = 10000, avg = 0.501457911440693, std = 0.289120988428389
0 - 0.1 - ***************************************
0.1 - 0.2 - ****************************************
0.2 - 0.3 - ****************************************
0.3 - 0.4 - ***************************************
0.4 - 0.5 - **************************************
0.5 - 0.6 - ***************************************
0.6 - 0.7 - *****************************************
0.7 - 0.8 - *****************************************
0.8 - 0.9 - ***************************************
0.9 - 1 - ****************************************
ok
>main(100000)
n = 100000, avg = 0.499807481461133, std = 0.28907281580804
0 - 0.1 - ****************************************
0.1 - 0.2 - ***************************************
0.2 - 0.3 - ***************************************
0.3 - 0.4 - ***************************************
0.4 - 0.5 - ***************************************
0.5 - 0.6 - ****************************************
0.6 - 0.7 - ***************************************
0.7 - 0.8 - ****************************************
0.8 - 0.9 - ***************************************
0.9 - 1 - ****************************************
ok
>main(1000000)
n = 1000000, avg = 0.500078448259022, std = 0.288580229525348
0 - 0.1 - ***************************************
0.1 - 0.2 - ****************************************
0.2 - 0.3 - ****************************************
0.3 - 0.4 - ****************************************
0.4 - 0.5 - ***************************************
0.5 - 0.6 - ****************************************
0.6 - 0.7 - ****************************************
0.7 - 0.8 - ****************************************
0.8 - 0.9 - ***************************************
0.9 - 1 - ***************************************
ok
>
</pre>
=={{header|PARI/GP}}==
{{works with|PARI/GP|2.4.3 and above}}
<syntaxhighlight lang="parigp">mean(v)={
vecsum(v)/#v
};
stdev(v,mu="")={
if(mu=="",mu=mean(v));
sqrt(sum(i=1,#v,(v[i]-mu)^2))/#v
};
histogram(v,bins=16,low=0,high=1)={
my(u=vector(bins),width=(high-low)/bins);
for(i=1,#v,u[(v[i]-low)\width+1]++);
u
};
show(n)={
my(v=vector(n,i,random(1.)),mu=mean(v),s=stdev(v,mu),h=histogram(v),sz=ceil(n/50/16));
for(i=1,16,for(j=1,h[i]\sz,print1("#"));print());
print("Mean: "mu);
print("Stdev: "s);
};
show(100);
show(1000);
show(10000);</syntaxhighlight>
For versions before 2.4.3, define
<syntaxhighlight lang="parigp">rreal()={
my(pr=32*ceil(default(realprecision)*log(10)/log(4294967296))); \\ Current precision
random(2^pr)*1.>>pr
};</syntaxhighlight>
and use <code>rreal()</code> in place of <code>random(1.)</code>.
=={{header|Perl}}==
<syntaxhighlight lang="perl">my @histogram = (0) x 10;
my $sum = 0;
my $sum_squares = 0;
my $n = $ARGV[0];
for (1..$n) {
my $current = rand();
$sum+= $current;
$sum_squares+= $current ** 2;
$histogram[$current * @histogram]+= 1;
}
my $mean = $sum / $n;
print "$n numbers\n",
"Mean: $mean\n",
"Stddev: ", sqrt(($sum_squares / $n) - ($mean ** 2)), "\n";
for my $i (0..$#histogram) {
printf "%.1f - %.1f : ", $i/@histogram, (1 + $i)/@histogram;
print "*" x (30 * $histogram[$i] * @histogram/$n); # 30 stars expected per row
print "\n";
}</syntaxhighlight>
Usage: <pre>perl rand_statistics.pl (number of values)</pre>
<pre>$ perl rand_statistics.pl 100
100 numbers
Mean: 0.531591369804339
Stddev: 0.28440375340793
0.0 - 0.1 : ***************************
0.1 - 0.2 : ************************
0.2 - 0.3 : ***************************
0.3 - 0.4 : ************************
0.4 - 0.5 : *********************************
0.5 - 0.6 : ************************************
0.6 - 0.7 : ************************************
0.7 - 0.8 : ******************
0.8 - 0.9 : ***************************************
0.9 - 1.0 : ************************************
$ perl rand_statistics.pl 1000
1000 numbers
Mean: 0.51011452684812
Stddev: 0.29490201218115
0.0 - 0.1 : ******************************
0.1 - 0.2 : *******************************
0.2 - 0.3 : ***************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : **********************************
0.5 - 0.6 : ****************************
0.6 - 0.7 : ************************
0.7 - 0.8 : *************************************
0.8 - 0.9 : ********************************
0.9 - 1.0 : *********************************
$ perl rand_statistics.pl 10000
10000 numbers
Mean: 0.495329167703333
Stddev: 0.285944419431566
0.0 - 0.1 : *****************************
0.1 - 0.2 : *******************************
0.2 - 0.3 : *********************************
0.3 - 0.4 : *******************************
0.4 - 0.5 : ******************************
0.5 - 0.6 : *******************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : ******************************
0.8 - 0.9 : *****************************
0.9 - 1.0 : ******************************
$ perl rand_statistics.pl 10000000
10000000 numbers
Mean: 0.499973935749229
Stddev: 0.2887231680817
0.0 - 0.1 : ******************************
0.1 - 0.2 : *******************************
0.2 - 0.3 : ******************************
0.3 - 0.4 : *******************************
0.4 - 0.5 : ******************************
0.5 - 0.6 : *******************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : ******************************
0.8 - 0.9 : *******************************
0.9 - 1.0 : *******************************</pre>
=={{header|Phix}}==
{{trans|CoffeeScript}}
To do a trillion samples, I would change the existing generate loop into an inner 100_000_000 loop that still uses the fast native types, with everything outside that changed to bigatom, and of course add an outer loop which sums into them.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">function</span> <span style="color: #000000;">generate_statistics</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">hist</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">sum_r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">sum_squares</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">rnd</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">sum_r</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">r</span>
<span style="color: #000000;">sum_squares</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">*</span><span style="color: #000000;">r</span>
<span style="color: #000000;">hist</span><span style="color: #0000FF;">[</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">*</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">mean</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">sum_r</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">stddev</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">((</span><span style="color: #000000;">sum_squares</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">*</span><span style="color: #000000;">mean</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stddev</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">hist</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">display_statistics</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stddev</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">hist</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">stddev</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">hist</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"-- Stats for sample size %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">n</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"mean: %g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">mean</span><span style="color: #0000FF;">})</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"sdev: %g\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">stddev</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">hist</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">cnt</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">hist</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">bars</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'='</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cnt</span><span style="color: #0000FF;">*</span><span style="color: #000000;">300</span><span style="color: #0000FF;">/</span><span style="color: #000000;">n</span><span style="color: #0000FF;">))</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%.1f: %s %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">bars</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cnt</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">5</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">display_statistics</span><span style="color: #0000FF;">(</span><span style="color: #000000;">generate_statistics</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">+(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">5</span><span style="color: #0000FF;">))))</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</syntaxhighlight>-->
{{Out}}
<pre style="float:left; font-size: 9px">
-- Stats for sample size 100
mean: 0.530925
sdev: 0.303564
0.1: ======================== 8
0.2: ======================================= 13
0.3: ============================== 10
0.4: ================== 6
0.5: ===================== 7
0.6: ================================= 11
0.7: ================================= 11
0.8: ===================== 7
0.9: ======================================= 13
1.0: ========================================== 14
</pre>
<pre style="float:left; font-size: 9px">
-- Stats for sample size 1000
mean: 0.50576
sdev: 0.288862
0.1: ============================ 95
0.2: ============================== 103
0.3: ============================= 98
0.4: =========================== 93
0.5: ============================== 101
0.6: ============================= 99
0.7: =============================== 105
0.8: ============================= 97
0.9: ================================ 108
1.0: ============================== 101
</pre>
<pre style="float:left; font-size: 9px">
-- Stats for sample size 10000
mean: 0.498831
sdev: 0.28841
0.1: ============================= 987
0.2: =============================== 1060
0.3: ============================ 953
0.4: ============================= 980
0.5: ============================== 1013
0.6: ============================= 997
0.7: ================================ 1089
0.8: ============================ 948
0.9: ============================= 974
1.0: ============================= 999
</pre>
<pre style="font-size: 9px">
-- Stats for sample size 1000000
mean: 0.499937
sdev: 0.288898
0.1: ============================== 100071
0.2: ============================== 100943
0.3: ============================= 99594
0.4: ============================= 99436
0.5: ============================= 99806
0.6: ============================= 99723
0.7: ============================== 100040
0.8: ============================== 100280
0.9: ============================== 100264
1.0: ============================= 99843
</pre>
=={{header|PicoLisp}}==
The following has no limit on the number of samples. The 'statistics' function accepts an executable body 'Prg', which it calls repeatedly to get the samples.
<syntaxhighlight lang="picolisp">
(seed (time))
(scl 8)
(de statistics (Cnt . Prg)
(prinl Cnt " numbers")
(let (Sum 0 Sqr 0 Hist (need 10 NIL 0))
(do Cnt
(let N (run Prg 1) # Get next number
(inc 'Sum N)
(inc 'Sqr (*/ N N 1.0))
(inc (nth Hist (inc (/ N 0.1)))) ) )
(let M (*/ Sum Cnt)
(prinl "Mean: " (round M))
(prinl "StdDev: "
(round
(sqrt
(- (*/ Sqr Cnt) (*/ M M 1.0))
1.0 ) ) ) )
(for (I . H) Hist
(prin (format I 1) " ")
(do (*/ H 400 Cnt) (prin '=))
(prinl) ) ) )
(for I (2 4 6)
(statistics (** 10 I)
(rand 0 (dec 1.0)) )
(prinl) )
</syntaxhighlight>
{{out}}
<pre>100 numbers
Mean: 0.501
StdDev: 0.284
0.1 ========================================
0.2 ====================================
0.3 ====================================================
0.4 ========================
0.5 ========================
0.6 ================================================================
0.7 ========================================================
0.8 ====================================
0.9 ========================
1.0 ============================================
10000 numbers
Mean: 0.501
StdDev: 0.288
0.1 =======================================
0.2 ========================================
0.3 =======================================
0.4 =========================================
0.5 =========================================
0.6 ========================================
0.7 =========================================
0.8 ========================================
0.9 ========================================
1.0 ========================================
1000000 numbers
Mean: 0.500
StdDev: 0.289
0.1 ========================================
0.2 ========================================
0.3 ========================================
0.4 ========================================
0.5 ========================================
0.6 ========================================
0.7 ========================================
0.8 ========================================
0.9 ========================================
1.0 ========================================</pre>
=={{header|PL/I}}==
<syntaxhighlight lang="pli"> stat: procedure options (main); /* 21 May 2014 */
stats: procedure (values, mean, standard_deviation);
declare (values(*), mean, standard_deviation) float;
declare n fixed binary (31) initial ( (hbound(values,1)) );
mean = sum(values)/n;
standard_deviation = sqrt( sum(values - mean)**2 / n);
end stats;
declare values (*) float controlled;
declare (mean, stddev) float;
declare bin(0:9) fixed;
declare (i, n) fixed binary (31);
do n = 100, 1000, 10000, 100000;
allocate values(n);
values = random();
call stats (values, mean, stddev);
if n = 100 then
do;
bin = 0;
do i = 1 to 100;
bin(10*values(i)) += 1;
end;
put skip list ('Histogram for 100 values:');
do i = 0 to 9; /* display histogram */
put skip list (repeat('.', bin(i)) );
end;
end;
put skip list (n || ' values: mean=' || mean, 'stddev=' || stddev);
free values;
end;
end stat;</syntaxhighlight>
{{out}}
<pre>Histogram for 100 values:
.......
..............
..............
...........
...............
........
...........
.........
.......
..............
100 values: mean= 4.89708E-0001 stddev= 1.64285E-0007
1000 values: mean= 4.97079E-0001 stddev= 1.07871E-0005
10000 values: mean= 4.99119E-0001 stddev= 8.35870E-0005
100000 values: mean= 5.00280E-0001 stddev= 7.88976E-0004 </pre>
=={{header|Python}}==
The second function, sd2 only needs to go once through the numbers and so can more efficiently handle large streams of numbers.
<
if numbers:
mean = sum(numbers) / len(numbers)
Line 192 ⟶ 4,472:
if __name__ == '__main__':
import random
for i in range(1,
n = [random.random() for
print("\n##\n## %i numbers\n##" % 10**i)
print(' Naive method: sd: %8.6f, mean: %8.6f' % sd1(n))
print(' Second method: sd: %8.6f, mean: %8.6f' % sd2(n))
histogram(n)</
{{out}}
for larger sets of random numbers,
the distribution of numbers between the bins of the histogram evens out.
<pre>...
##
Line 237 ⟶ 4,518:
0.8: +++++++++++++++++++++++++++++++++++++++++++++++++
0.9: +++++++++++++++++++++++++++++++++++++++++++++++++</pre>
=={{header|R}}==
The challenge of processing a trillion numbers is generating them in the first place. As the errors below show, allocating 7.5 TB for such a vector is simply impractical. The workaround is to generate them, process individual data points and then discard them. The downside in this case is the time.
<syntaxhighlight lang="r">
#Generate the sets
a = runif(10,min=0,max=1)
b = runif(100,min=0,max=1)
c = runif(1000,min=0,max=1)
d = runif(10000,min=0,max=1)
#Print out the set of 10 values
cat("a = ",a)
#Print out the Mean and Standard Deviations of each of the sets
cat("Mean of a : ",mean(a))
cat("Standard Deviation of a : ", sd(a))
cat("Mean of b : ",mean(b))
cat("Standard Deviation of b : ", sd(b))
cat("Mean of c : ",mean(c))
cat("Standard Deviation of c : ", sd(c))
cat("Mean of d : ",mean(d))
cat("Standard Deviation of d : ", sd(d))
#Plotting the histogram of d
hist(d)
#Following lines error out due to insufficient memory
cat("Mean of a trillion random values in the range [0,1] : ",mean(runif(10^12,min=0,max=1)))
cat("Standard Deviation of a trillion random values in the range [0,1] : ", sd(runif(10^12,min=0,max=1)))
</syntaxhighlight>
Output
<pre>
a = 0.3884718 0.6324655 0.9288667 0.1948398 0.5636742 0.2746207 0.4712035 0.2624648 0.45492 0.3328236>
Mean of a : 0.4504351
Standard Deviation of a : 0.2171919
Mean of b : 0.5240795
Standard Deviation of b : 0.2654211
Mean of c : 0.5000978
Standard Deviation of c : 0.2882098
Mean of d : 0.4991501
Standard Deviation of d : 0.2911486
Error: cannot allocate vector of size 7450.6 Gb
Error: cannot allocate vector of size 7450.6 Gb
</pre>
=={{header|Racket}}==
<syntaxhighlight lang="racket">
#lang racket
(require math (only-in srfi/27 random-real))
(define (histogram n xs Δx)
(define (r x) (~r x #:precision 1 #:min-width 3))
(define (len count) (exact-floor (/ (* count 200) n)))
(for ([b (bin-samples (range 0 1 Δx) <= xs)])
(displayln (~a (r (sample-bin-min b)) "-" (r (sample-bin-max b)) ": "
(make-string (len (length (sample-bin-values b))) #\*)))))
(define (task n)
(define xs (for/list ([_ n]) (random-real)))
(displayln (~a "Number of samples: " n))
(displayln (~a "Mean: " (mean xs)))
(displayln (~a "Standard deviance: " (stddev xs)))
(histogram n xs 0.1)
(newline))
(task 100)
(task 1000)
(task 10000)
</syntaxhighlight>
{{out}}
<pre>
Number of samples: 100
Mean: 0.5466640451797568
Standard deviance: 0.29309099509716496
0-0.1: ************
0.1-0.2: ************************
0.2-0.3: ********************
0.3-0.4: ************
0.4-0.5: ****************
0.5-0.6: ********************
0.6-0.7: ********************
0.7-0.8: **************************
0.8-0.9: **************************
0.9- 1: ************************
Number of samples: 1000
Mean: 0.48116201801707503
Standard deviance: 0.2873408579602762
0-0.1: *********************
0.1-0.2: *********************
0.2-0.3: ********************
0.3-0.4: ***********************
0.4-0.5: *******************
0.5-0.6: *******************
0.6-0.7: *******************
0.7-0.8: *****************
0.8-0.9: ******************
0.9- 1: ******************
Number of samples: 10000
Mean: 0.4988839808467469
Standard deviance: 0.2892924816935072
0-0.1: ********************
0.1-0.2: *******************
0.2-0.3: ********************
0.3-0.4: *******************
0.4-0.5: *******************
0.5-0.6: ********************
0.6-0.7: ********************
0.7-0.8: *******************
0.8-0.9: ********************
0.9- 1: *******************
</pre>
=={{header|Raku}}==
(formerly Perl 6)
{{Works with|rakudo|2018.03}}
<syntaxhighlight lang="raku" line>for 100, 1_000, 10_000 -> $N {
say "size: $N";
my @data = rand xx $N;
printf "mean: %f\n", my $mean = $N R/ [+] @data;
printf "stddev: %f\n", sqrt
$mean**2 R- $N R/ [+] @data »**» 2;
printf "%.1f %s\n", .key, '=' x (500 * .value.elems / $N)
for sort @data.classify: (10 * *).Int / 10;
say '';
}</syntaxhighlight>
{{out}}
<pre>size: 100
mean: 0.52518699464629726
stddev: 0.28484207464779548
0.0 ==============================
0.1 ======================================================================
0.2 ===================================
0.3 ==================================================
0.4 ============================================================
0.5 =============================================
0.6 ====================
0.7 ===========================================================================
0.8 ======================================================================
0.9 =============================================
size: 1000
mean: 0.51043974182914975
stddev: 0.29146336553431618
0.0 ==============================================
0.1 ==================================================
0.2 ===========================================
0.3 ========================================================
0.4 ===================================================
0.5 =======================================
0.6 ===========================================================
0.7 ====================================================
0.8 ==============================================
0.9 ========================================================
size: 10000
mean: 0.50371817503544458
stddev: 0.2900716333092252
0.0 ===================================================
0.1 =================================================
0.2 =============================================
0.3 ====================================================
0.4 ==============================================
0.5 ====================================================
0.6 ================================================
0.7 ===================================================
0.8 ====================================================
0.9 ==================================================</pre>
=={{header|REXX}}==
Twenty decimal digits are used for the calculations, but only half that (ten digits) are displayed in the output.
<syntaxhighlight lang="rexx">/*REXX program generates some random numbers, shows bin histogram, finds mean & stdDev. */
numeric digits 20 /*use twenty decimal digits precision, */
showDigs=digits()%2 /* ··· but only show ten decimal digits*/
parse arg size seed . /*allow specification: size, and seed.*/
if size=='' | size=="," then size=100 /*Not specified? Then use the default.*/
if datatype(seed,'W') then call random ,,seed /*allow a seed for the RANDOM BIF. */
#.=0 /*count of the numbers in each bin. */
do j=1 for size /*generate some random numbers. */
@.j=random(, 99999) / 100000 /*express random number as a fraction. */
_=substr(@.j'00', 3, 1) /*determine which bin the number is in,*/
#._=#._ + 1 /* ··· and bump its count. */
end /*j*/
do k=0 for 10; kp=k + 1 /*show a histogram of the bins. */
lr='0.'k ; if k==0 then lr= "0 " /*adjust for the low range. */
hr='0.'kp ; if k==9 then hr= "1 " /* " " " high range. */
barPC=right( strip( left( format( 100*#.k / size, , 2), 5)), 5) /*compute the %. */
say lr"──►"hr' ' barPC copies("─", barPC * 2 % 1 ) /*show histogram.*/
end /*k*/
say
say 'sample size = ' size; say
avg= mean(size) ; say ' mean = ' format(avg, , showDigs)
std=stdDev(size) ; say ' stdDev = ' format(std, , showDigs)
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
mean: arg N; $=0; do m=1 for N; $=$ + @.m; end; return $/N
stdDev: arg N; $=0; do s=1 for N; $=$ + (@.s-avg)**2; end; return sqrt($/N) /1
/*──────────────────────────────────────────────────────────────────────────────────────*/
sqrt: procedure; parse arg x; if x=0 then return 0; d=digits(); m.=9; numeric form; h=d+6
numeric digits; parse value format(x,2,1,,0) 'E0' with g 'E' _ .; g=g*.5'e'_ % 2
do j=0 while h>9; m.j=h; h=h%2+1; end /*j*/
do k=j+5 to 0 by -1; numeric digits m.k; g=(g+x/g)*.5; end /*k*/; return g</syntaxhighlight>
{{out|output|text= when using the default input of: <tt> 100 </tt>}}
<pre>
0 ──►0.1 12.00 ────────────────────────
0.1──►0.2 12.00 ────────────────────────
0.2──►0.3 10.00 ────────────────────
0.3──►0.4 8.00 ────────────────
0.4──►0.5 12.00 ────────────────────────
0.5──►0.6 8.00 ────────────────
0.6──►0.7 11.00 ──────────────────────
0.7──►0.8 11.00 ──────────────────────
0.8──►0.9 6.00 ────────────
0.9──►1 10.00 ────────────────────
sample size = 100
mean = 0.4711358000
stdDev = 0.2920169478
</pre>
{{out|output|text= when using the default input of: <tt> 1000 </tt>}}
<pre>
0 ──►0.1 9.50 ───────────────────
0.1──►0.2 9.90 ───────────────────
0.2──►0.3 11.70 ───────────────────────
0.3──►0.4 8.80 ─────────────────
0.4──►0.5 8.40 ────────────────
0.5──►0.6 10.20 ────────────────────
0.6──►0.7 10.30 ────────────────────
0.7──►0.8 11.40 ──────────────────────
0.8──►0.9 9.10 ──────────────────
0.9──►1 10.70 ─────────────────────
sample size = 1000
mean = 0.5037752500
stdDev = 0.2886365539
</pre>
{{out|output|text= when using the default input of: <tt> 10000 </tt>}}
<pre>
0 ──►0.1 9.61 ───────────────────
0.1──►0.2 10.45 ────────────────────
0.2──►0.3 9.96 ───────────────────
0.3──►0.4 10.56 ─────────────────────
0.4──►0.5 9.91 ───────────────────
0.5──►0.6 10.13 ────────────────────
0.6──►0.7 10.12 ────────────────────
0.7──►0.8 9.84 ───────────────────
0.8──►0.9 9.61 ───────────────────
0.9──►1 9.81 ───────────────────
sample size = 10000
mean = 0.4968579550
stdDev = 0.2863756713
</pre>
{{out|output|text= when using the default input of: <tt> 100000 </tt>}}
<pre>
0 ──►0.1 10.13 ────────────────────
0.1──►0.2 9.84 ───────────────────
0.2──►0.3 9.91 ───────────────────
0.3──►0.4 9.94 ───────────────────
0.4──►0.5 10.19 ────────────────────
0.5──►0.6 10.08 ────────────────────
0.6──►0.7 10.12 ────────────────────
0.7──►0.8 9.78 ───────────────────
0.8──►0.9 10.07 ────────────────────
0.9──►1 9.95 ───────────────────
sample size = 100000
mean = 0.4999883642
stdDev = 0.2884109515
</pre>
{{out|output|text= when using the default input of: <tt> 1000000 </tt>}}
<pre>
0 ──►0.1 9.94 ───────────────────
0.1──►0.2 10.03 ────────────────────
0.2──►0.3 10.03 ────────────────────
0.3──►0.4 9.98 ───────────────────
0.4──►0.5 10.00 ────────────────────
0.5──►0.6 10.03 ────────────────────
0.6──►0.7 9.99 ───────────────────
0.7──►0.8 10.03 ────────────────────
0.8──►0.9 9.97 ───────────────────
0.9──►1 9.99 ───────────────────
sample size = 1000000
mean = 0.5000687045
stdDev = 0.2885125537
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
# Project : Statistics/Basic
decimals(9)
sample(100)
sample(1000)
sample(10000)
func sample(n)
samp = list(n)
for i =1 to n
samp[i] =random(9)/10
next
sum = 0
sumSq = 0
for i = 1 to n
sum = sum + samp[i]
sumSq = sumSq +pow(samp[i],2)
next
see n + " Samples used." + nl
mean = sum / n
see "Mean = " + mean + nl
see "Std Dev = " + pow((sumSq /n -pow(mean,2)),0.5) + nl
bins2 = 10
bins = list(bins2)
for i = 1 to n
z = floor(bins2 * samp[i])
if z != 0
bins[z] = bins[z] +1
ok
next
for b = 1 to bins2
see b + " " + nl
for j = 1 to floor(bins2 *bins[b]) /n *70
see "*"
next
see nl
next
see nl
</syntaxhighlight>
Output:
<pre>
100
Mean = 0.482000000
Std Dev = 0.276904316
1
***************************************************************
2
********************************************************
3
********************************************************
4
*****************************************************************************
5
**********************************************************************
6
*****************************************************************************
7
***********************************************************************************************************************
8
********************************************************
9
**********************************************************************
1000
Mean = 0.436600000
Std Dev = 0.284605762
1
*******************************************************************************
2
**********************************************************************
3
***********************************************************************************
4
************************************************************************
5
***********************************************************************
6
******************************************************************
7
*******************************************************
8
****************************************************************
9
**********************************************************************
10000
Mean = 0.451940000
Std Dev = 0.287183280
1
********************************************************************
2
***********************************************************************
3
*******************************************************************
4
*********************************************************************
5
*********************************************************************
6
***********************************************************************
7
*********************************************************************
8
************************************************************************
9
*********************************************************************
</pre>
=={{header|RPL}}==
Built-in statistics functions in RPL relies on a specific array named <code>∑DAT</code>, which is automatically generated when the first record is created by the word <code>∑+</code>.
{{works with|Halcyon Calc|4.2.8}}
{| class="wikitable"
! RPL code
! Comment
|-
|
≪ → n
≪ CL∑ 1 n '''START''' RAND ∑+ '''NEXT'''
MEAN SDEV
{ 10 } 0 CON
1 n '''FOR''' j
∑DAT j { 1 } + GET
10 * 1 + FLOOR DUP2 GET 1 + PUT
'''NEXT'''
{ } 1 10 '''FOR''' j
OVER j GET 3 PICK RNRM / 20 *
"0." j 1 - →STR + "= " + 1 ROT '''START''' "*" + '''NEXT''' +
'''NEXT'''
≫ ≫ ‘<span style="color:blue">TASK</span>’ STO
|
<span style="color:blue">TASK</span> ''( #samples → statistics... ) ''
Generate and store samples in the statistics database
The easy part of the task
Create a 10-cell vector
Scan the database
Read the nth record
Increment the related cell
Generate histogramme
RNRM returns the max value of the 10-cell vector
|}
1000 <span style="color:blue">TASK</span>
{{out}}
<pre>
4: 0.492756012687
3: 0.29333176137
2: [ 120 100 90 86 112 113 90 87 97 105 ]
1: { "0.0= ********************"
"0.1= ****************"
"0.2= ***************"
"0.3= **************"
"0.4= ******************"
"0.5= ******************"
"0.6= ***************"
"0.7= **************"
"0.8= ****************"
"0.9= *****************" }
</pre>
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">def generate_statistics(n)
sum = sum2 = 0.0
hist = Array.new(10, 0)
n.times do
r = rand
sum += r
sum2 += r**2
hist[(10*r).to_i] += 1
end
mean = sum / n
stddev = Math::sqrt((sum2 / n) - mean**2)
puts "size: #{n}"
puts "mean: #{mean}"
puts "stddev: #{stddev}"
hist.each_with_index {|x,i| puts "%.1f:%s" % [0.1*i, "=" * (70*x/hist.max)]}
puts
end
[100, 1000, 10000].each {|n| generate_statistics n}</syntaxhighlight>
{{out}}
<pre style="height: 40ex; overflow: scroll">size: 100
mean: 0.5565132836634081
stddev: 0.30678831716883026
0.0:================================
0.1:============================================================
0.2:================================
0.3:============================
0.4:==============================================
0.5:=======================
0.6:========================================================
0.7:========================================================
0.8:============================================================
0.9:======================================================================
size: 1000
mean: 0.4910962662424557
stddev: 0.28325915710008404
0.0:======================================================
0.1:==================================================
0.2:=======================================================
0.3:======================================================================
0.4:=====================================================
0.5:=================================================
0.6:=================================================
0.7:=============================================================
0.8:================================================
0.9:=================================================
size: 10000
mean: 0.5036461506004852
stddev: 0.28754747617166443
0.0:==============================================================
0.1:=================================================================
0.2:====================================================================
0.3:================================================================
0.4:================================================================
0.5:=================================================================
0.6:======================================================================
0.7:===================================================================
0.8:===================================================================
0.9:=================================================================</pre>
=={{header|Rust}}==
{{libheader|rand}}
<syntaxhighlight lang="rust">#![feature(iter_arith)]
extern crate rand;
use rand::distributions::{IndependentSample, Range};
pub fn mean(data: &[f32]) -> Option<f32> {
if data.is_empty() {
None
} else {
let sum: f32 = data.iter().sum();
Some(sum / data.len() as f32)
}
}
pub fn variance(data: &[f32]) -> Option<f32> {
if data.is_empty() {
None
} else {
let mean = mean(data).unwrap();
let mut sum = 0f32;
for &x in data {
sum += (x - mean).powi(2);
}
Some(sum / data.len() as f32)
}
}
pub fn standard_deviation(data: &[f32]) -> Option<f32> {
if data.is_empty() {
None
} else {
let variance = variance(data).unwrap();
Some(variance.sqrt())
}
}
fn print_histogram(width: u32, data: &[f32]) {
let mut histogram = [0; 10];
let len = histogram.len() as f32;
for &x in data {
histogram[(x * len) as usize] += 1;
}
let max_frequency = *histogram.iter().max().unwrap() as f32;
for (i, &frequency) in histogram.iter().enumerate() {
let bar_width = frequency as f32 * width as f32 / max_frequency;
print!("{:3.1}: ", i as f32 / len);
for _ in 0..bar_width as usize {
print!("*");
}
println!("");
}
}
fn main() {
let range = Range::new(0f32, 1f32);
let mut rng = rand::thread_rng();
for &number_of_samples in [1000, 10_000, 1_000_000].iter() {
let mut data = vec![];
for _ in 0..number_of_samples {
let x = range.ind_sample(&mut rng);
data.push(x);
}
println!(" Statistics for sample size {}", number_of_samples);
println!("Mean: {:?}", mean(&data));
println!("Variance: {:?}", variance(&data));
println!("Standard deviation: {:?}", standard_deviation(&data));
print_histogram(40, &data);
}
}</syntaxhighlight>
{{out}}
<pre> Statistics for sample size 1000
Mean: Some(0.50145197)
Variance: Some(0.08201705)
Standard deviation: Some(0.2863862)
0.0: *********************************
0.1: ****************************
0.2: **********************************
0.3: ************************************
0.4: **************************************
0.5: *********************************
0.6: ******************************
0.7: ******************************
0.8: ****************************************
0.9: ******************************
Statistics for sample size 10000
Mean: Some(0.49700406)
Variance: Some(0.08357173)
Standard deviation: Some(0.28908777)
0.0: **************************************
0.1: ***************************************
0.2: ***************************************
0.3: ***************************************
0.4: ***********************************
0.5: ***************************************
0.6: *************************************
0.7: ****************************************
0.8: **************************************
0.9: *************************************
Statistics for sample size 1000000
Mean: Some(0.50038373)
Variance: Some(0.08325759)
Standard deviation: Some(0.2885439)
0.0: ***************************************
0.1: ***************************************
0.2: ***************************************
0.3: ****************************************
0.4: ***************************************
0.5: ***************************************
0.6: ***************************************
0.7: ***************************************
0.8: ***************************************
0.9: ***************************************</pre>
=={{header|Scala}}==
<syntaxhighlight lang="scala">def mean(a:Array[Double])=a.sum / a.size
def stddev(a:Array[Double])={
val sum = a.fold(0.0)((a, b) => a + math.pow(b,2))
math.sqrt((sum/a.size) - math.pow(mean(a),2))
}
def hist(a:Array[Double]) = {
val grouped=(SortedMap[Double, Array[Double]]() ++ (a groupBy (x => math.rint(x*10)/10)))
grouped.map(v => (v._1, v._2.size))
}
def printHist(a:Array[Double])=for((g,v) <- hist(a)){
println(s"$g: ${"*"*(205*v/a.size)} $v")
}
for(n <- Seq(100,1000,10000)){
val a = Array.fill(n)(Random.nextDouble)
println(s"$n numbers")
println(s"Mean: ${mean(a)}")
println(s"StdDev: ${stddev(a)}")
printHist(a)
println
}</syntaxhighlight>
{{out}}
<pre>100 numbers
Mean: 0.5151424022100874
StdDev: 0.25045766440922146
0.0: **** 2
0.1: **************** 8
0.2: **************** 8
0.3: ******************** 10
0.4: ************************ 12
0.5: ****************************** 15
0.6: ****************************** 15
0.7: **************** 8
0.8: ******************** 10
0.9: ********************** 11
1.0: ** 1
1000 numbers
Mean: 0.4954605718792786
StdDev: 0.28350795290401604
0.0: ********* 48
0.1: ******************* 93
0.2: *********************** 117
0.3: ******************** 99
0.4: ***************** 87
0.5: ********************** 108
0.6: ************************* 122
0.7: ****************** 88
0.8: ******************** 100
0.9: ****************** 88
1.0: ********** 50
10000 numbers
Mean: 0.502395544726441
StdDev: 0.2874443665645294
0.0: ********** 496
0.1: ******************** 979
0.2: ******************* 962
0.3: ******************** 1010
0.4: ******************** 998
0.5: ********************* 1035
0.6: ******************** 984
0.7: ********************* 1031
0.8: ********************* 1027
0.9: ******************** 991
1.0: ********* 487</pre>
=={{header|Sidef}}==
{{trans|Ruby}}
<syntaxhighlight lang="ruby">func generate_statistics(n) {
var(sum=0, sum2=0)
var hist = 10.of(0)
n.times {
var r = 1.rand
sum += r
sum2 += r**2
hist[10*r] += 1
}
var mean = sum/n
var stddev = sqrt(sum2/n - mean**2)
say "size: #{n}"
say "mean: #{mean}"
say "stddev: #{stddev}"
var max = hist.max
for i in ^hist {
printf("%.1f:%s\n", 0.1*i, "=" * 70*hist[i]/max)
}
print "\n"
}
[100, 1000, 10000].each {|n| generate_statistics(n) }</syntaxhighlight>
{{out}}
<pre style="height: 40ex; overflow: scroll">
size: 100
mean: 0.539719181395696620109634051345884432579835159541
stddev: 0.283883840711089795862044996985935095942987013707
0.0:====================================================
0.1:=============================
0.2:====================================================
0.3:======================================================================
0.4:==========================================================
0.5:======================================================================
0.6:==============================================
0.7:======================================================================
0.8:======================================================================
0.9:================================================================
size: 1000
mean: 0.509607463325018405029035982604757578351179500375
stddev: 0.291051486526422985516729469185300756396357843712
0.0:==========================================================
0.1:========================================================
0.2:================================================================
0.3:========================================================
0.4:======================================================
0.5:=====================================================================
0.6:========================================================
0.7:===========================================================
0.8:==========================================================
0.9:======================================================================
size: 10000
mean: 0.501370967820671948202377775772729161752514666335
stddev: 0.288601021921015908441703525737039264149088197141
0.0:===============================================================
0.1:====================================================================
0.2:==================================================================
0.3:=================================================================
0.4:======================================================================
0.5:=================================================================
0.6:===============================================================
0.7:===================================================================
0.8:==================================================================
0.9:====================================================================
</pre>
=={{header|Stata}}==
For a uniform distribution on [0,1], the mean is 1/2 and the variance is 1/12 (hence the standard deviation is 0.28867513). With a large sample, one can check the convergence to these values.
<syntaxhighlight lang="stata">. clear all
. set obs 100000
number of observations (_N) was 0, now 100,000
. gen x=runiform()
. summarize x
Variable | Obs Mean Std. Dev. Min Max
-------------+---------------------------------------------------------
x | 100,000 .4991874 .2885253 1.18e-06 .9999939
. hist x</syntaxhighlight>
=={{header|Tcl}}==
<syntaxhighlight lang="tcl">package require Tcl 8.5
proc stats {size} {
set sum 0.0
set sum2 0.0
for {set i 0} {$i < $size} {incr i} {
set r [expr {rand()}]
incr histo([expr {int(floor($r*10))}])
set sum [expr {$sum + $r}]
set sum2 [expr {$sum2 + $r**2}]
}
set mean [expr {$sum / $size}]
set stddev [expr {sqrt($sum2/$size - $mean**2)}]
puts "$size numbers"
puts "Mean: $mean"
puts "StdDev: $stddev"
foreach i {0 1 2 3 4 5 6 7 8 9} {
# The 205 is a magic factor stolen from the Go solution
puts [string repeat "*" [expr {$histo($i)*205/int($size)}]]
}
}
stats 100
puts ""
stats 1000
puts ""
stats 10000</syntaxhighlight>
{{out}}
<pre>
100 numbers
Mean: 0.4801193240797704
StdDev: 0.28697057708153784
**************
**********************************
********************
**************
****************************
****************
**************
****************************
****************
****************
1000 numbers
Mean: 0.49478823525495275
StdDev: 0.2821543810265757
*******************
******************
************************
********************
*******************
**********************
*********************
********************
******************
******************
10000 numbers
Mean: 0.49928563715870816
StdDev: 0.2888258479070212
********************
*********************
********************
********************
*******************
*********************
*******************
********************
*********************
********************
</pre>
As can be seen, increasing the sample size reduces the variation between the buckets, showing that the <code>rand()</code> function at least approximates a uniform distribution. (Because Tcl 8.5 supports arbitrary precision integer arithmetic there is no reason in principle why the details for a trillion numbers couldn't be calculated, but it would take quite a while.)
=={{header|VBA}}==
<syntaxhighlight lang="vb">Option Base 1
Private Function mean(s() As Variant) As Double
mean = WorksheetFunction.Average(s)
End Function
Private Function standard_deviation(s() As Variant) As Double
standard_deviation = WorksheetFunction.StDev(s)
End Function
Public Sub basic_statistics()
Dim s() As Variant
For e = 2 To 4
ReDim s(10 ^ e)
For i = 1 To 10 ^ e
s(i) = Rnd()
Next i
Debug.Print "sample size"; UBound(s), "mean"; mean(s), "standard deviation"; standard_deviation(s)
t = WorksheetFunction.Frequency(s, [{0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0}])
For i = 1 To 10
Debug.Print Format((i - 1) / 10, "0.00");
Debug.Print "-"; Format(i / 10, "0.00"),
Debug.Print String$(t(i, 1) / (10 ^ (e - 2)), "X");
Debug.Print
Next i
Debug.Print
Next e
End Sub</syntaxhighlight>{{out}}
<pre>sample size 100 mean 0,472405961751938 standard deviation 0,260463885857138
0,00-0,10 XXXXXX
0,10-0,20 XXXXXXXXX
0,20-0,30 XXXXXXXXXXXXXXX
0,30-0,40 XXXXXXXXXXXXXXX
0,40-0,50 XXXXXXXXXXXXXX
0,50-0,60 XXXXXXX
0,60-0,70 XXXXXXXXXXX
0,70-0,80 XXXXXXXX
0,80-0,90 XXXXXXXXXX
0,90-1,00 XXXXX
sample size 1000 mean 0,500459910154343 standard deviation 0,278991757028358
0,00-0,10 XXXXXXXX
0,10-0,20 XXXXXXXXXX
0,20-0,30 XXXXXXXXXX
0,30-0,40 XXXXXXXXXX
0,40-0,50 XXXXXXXXXX
0,50-0,60 XXXXXXXXXXXX
0,60-0,70 XXXXXXXXXXX
0,70-0,80 XXXXXXXXX
0,80-0,90 XXXXXXXXX
0,90-1,00 XXXXXXXXXX
sample size 10000 mean 0,496753623914719 standard deviation 0,28740805585887
0,00-0,10 XXXXXXXXXX
0,10-0,20 XXXXXXXXXX
0,20-0,30 XXXXXXXXXX
0,30-0,40 XXXXXXXXXX
0,40-0,50 XXXXXXXXXX
0,50-0,60 XXXXXXXXXX
0,60-0,70 XXXXXXXXXX
0,70-0,80 XXXXXXXXXX
0,80-0,90 XXXXXXXXXX
0,90-1,00 XXXXXXXXXX</pre>
=={{header|V (Vlang)}}==
{{trans|go}}
<syntaxhighlight lang="v (vlang)">import rand
import math
fn main() {
sample(100)
sample(1000)
sample(10000)
}
fn sample(n int) {
// generate data
mut d := []f64{len: n}
for i in 0.. d.len {
d[i] = rand.f64()
}
// show mean, standard deviation
mut sum, mut ssq := f64(0), f64(0)
for s in d {
sum += s
ssq += s * s
}
println("$n numbers")
m := sum / f64(n)
println("Mean: $m")
println("Stddev: ${math.sqrt(ssq/f64(n)-m*m)}")
// show histogram
mut h := []int{len: 10}
for s in d {
h[int(s*10)]++
}
for c in h {
println("*".repeat(c*205/int(n)))
}
println('')
}</syntaxhighlight>
{{out}}
Sample run:
<pre>
100 numbers
Mean: 0.4673526451482236
Stddev: 0.27590441169077806
****************
********************************
********************
********************
************
******************************
************
**********************************
**********
**************
1000 numbers
Mean: 0.4906097518067266
Stddev: 0.28686496927912264
********************
*********************
**********************
*********************
********************
*****************
*******************
*********************
********************
******************
10000 numbers
Mean: 0.5012521647492316
Stddev: 0.2883488134311142
********************
********************
*********************
******************
*********************
*********************
********************
********************
********************
********************
</pre>
Or use standard math.stats module
<syntaxhighlight lang="text">import rand
import math.stats
fn main() {
sample(100)
sample(1000)
sample(10000)
}
fn sample(n int) {
// generate data
mut d := []f64{len: n}
for i in 0.. d.len {
d[i] = rand.f64()
}
// show mean, standard deviation
println("$n numbers")
m := stats.mean<f64>(d)//sum / f64(n)
println("Mean: $m")
println("Stddev: ${stats.sample_stddev<f64>(d)}")
// show histogram
mut h := []int{len: 10}
for s in d {
h[int(s*10)]++
}
for c in h {
println("*".repeat(c*205/int(n)))
}
println('')
}</syntaxhighlight>
{{out}}
Similar to above
=={{header|Wren}}==
{{libheader|Wren-math}}
<syntaxhighlight lang="wren">import "random" for Random
import "./math" for Nums
var r = Random.new()
for (i in [100, 1000, 10000]) {
var a = List.filled(i, 0)
for (j in 0...i) a[j] = r.float()
System.print("For %(i) random numbers:")
System.print(" mean = %(Nums.mean(a))")
System.print(" std/dev = %(Nums.popStdDev(a))")
var scale = i / 100
System.print(" scale = %(scale) per asterisk")
var sums = List.filled(10, 0)
for (e in a) {
var f = (e*10).floor
sums[f] = sums[f] + 1
}
for (j in 0..8) {
sums[j] = (sums[j] / scale).round
System.print(" 0.%(j) - 0.%(j+1): %("*" * sums[j])")
}
sums[9] = 100 - Nums.sum(sums[0..8])
System.print(" 0.9 - 1.0: %("*" * sums[9])\n")
}</syntaxhighlight>
{{out}}
Sample run:
<pre>
For 100 random numbers:
mean = 0.51850420177277
std/dev = 0.28837198153139
scale = 1 per asterisk
0.0 - 0.1: ***********
0.1 - 0.2: ******
0.2 - 0.3: **********
0.3 - 0.4: *********
0.4 - 0.5: *********
0.5 - 0.6: ***********
0.6 - 0.7: ************
0.7 - 0.8: ***********
0.8 - 0.9: ********
0.9 - 1.0: *************
For 1000 random numbers:
mean = 0.50563060529132
std/dev = 0.28829500547546
scale = 10 per asterisk
0.0 - 0.1: *********
0.1 - 0.2: **********
0.2 - 0.3: **********
0.3 - 0.4: **********
0.4 - 0.5: ********
0.5 - 0.6: ***********
0.6 - 0.7: ***********
0.7 - 0.8: *********
0.8 - 0.9: *********
0.9 - 1.0: *************
For 10000 random numbers:
mean = 0.5037035497178
std/dev = 0.28753708198548
scale = 100 per asterisk
0.0 - 0.1: **********
0.1 - 0.2: **********
0.2 - 0.3: **********
0.3 - 0.4: **********
0.4 - 0.5: **********
0.5 - 0.6: **********
0.6 - 0.7: **********
0.7 - 0.8: **********
0.8 - 0.9: **********
0.9 - 1.0: **********
</pre>
=={{header|XPL0}}==
{{trans|Wren}}
<syntaxhighlight lang "XPL0">include xpllib; \for Print
func real Mean(X, N);
real X; int N;
real Sum; int I;
[Sum:= 0.;
for I:= 0 to N-1 do
Sum:= Sum + X(I);
return Sum/float(N);
];
func real StdDev(X, N, Mean);
real X; int N; real Mean;
real Sum; int I;
[Sum:= 0.;
for I:= 0 to N-1 do
Sum:= Sum + sq(X(I) - Mean);
return sqrt(Sum/float(N));
];
int Size, J, K, Sums(10), Scale;
real A, M;
[Size:= 100;
repeat A:= RlRes(Size);
for J:= 0 to Size-1 do
A(J):= float(Ran(1_000_000)) / 1e6;
Print("For %d random numbers:\n", Size);
M:= Mean(A, Size);
Print(" mean = %1.9f\n", M);
Print(" stddev = %1.9f\n", StdDev(A, Size, M));
Scale:= Size / 100;
Print(" scale = %d per asterisk\n", Scale);
for J:= 0 to 10-1 do Sums(J):= 0;
for J:= 0 to Size-1 do
[K:= fix(Floor(A(J)*10.));
Sums(K):= Sums(K)+1;
];
for J:= 0 to 8 do
[Sums(J):= Sums(J) / Scale;
Print(" 0.%d - 0.%d: ", J, J+1);
for K:= 1 to Sums(J) do ChOut(0, ^*);
CrLf(0);
];
Print(" 0.9 - 1.0: ");
for K:= 1 to Sums(9)/Scale do ChOut(0, ^*);
CrLf(0); CrLf(0);
Size:= Size * 10;
until Size > 10_000;
]</syntaxhighlight>
{{out}}
<pre>
For 100 random numbers:
mean = 0.516471700
stddev = 0.286590092
scale = 1 per asterisk
0.0 - 0.1: *********
0.1 - 0.2: ***********
0.2 - 0.3: ********
0.3 - 0.4: ********
0.4 - 0.5: **************
0.5 - 0.6: ***
0.6 - 0.7: **********
0.7 - 0.8: ******************
0.8 - 0.9: *********
0.9 - 1.0: **********
For 1000 random numbers:
mean = 0.485343800
stddev = 0.287769421
scale = 10 per asterisk
0.0 - 0.1: **********
0.1 - 0.2: ***********
0.2 - 0.3: *********
0.3 - 0.4: ***********
0.4 - 0.5: *********
0.5 - 0.6: ***********
0.6 - 0.7: ********
0.7 - 0.8: *********
0.8 - 0.9: ********
0.9 - 1.0: **********
For 10000 random numbers:
mean = 0.501502304
stddev = 0.288991280
scale = 100 per asterisk
0.0 - 0.1: *********
0.1 - 0.2: **********
0.2 - 0.3: **********
0.3 - 0.4: *********
0.4 - 0.5: *********
0.5 - 0.6: *********
0.6 - 0.7: **********
0.7 - 0.8: **********
0.8 - 0.9: **********
0.9 - 1.0: **********
</pre>
=={{header|zkl}}==
<syntaxhighlight lang="zkl">fcn mean(ns) { ns.sum(0.0)/ns.len() }
fcn stdDev(ns){
m:=mean(ns); (ns.reduce('wrap(p,n){ x:=(n-m); p+x*x },0.0)/ns.len()).sqrt()
}</syntaxhighlight>
<syntaxhighlight lang="zkl">reg ns;
foreach n in (T(100,1000,10000)){
ns=(0).pump(n,List,(0.0).random.fp(1.0));
println("N:%,6d mean:%.5f std dev:%.5f".fmt(n,mean(ns),stdDev(ns)));
}
foreach r in ([0.0 .. 0.9, 0.1]){ // using the last data set (10000 randoms)
n:=ns.filter('wrap(x){ r<=x<(r+0.1) }).len();
println("%.2f..%.2f:%4d%s".fmt(r,r+0.1,n,"*"*(n/20)));
}</syntaxhighlight>
(0.0).random(1.0) generates a [uniform] random number between 0 (inclusive) and 1 (exclusive).
{{out}}
<pre>
N: 100 mean:0.48521 std dev:0.27073
N: 1,000 mean:0.49362 std dev:0.28921
N:10,000 mean:0.49899 std dev:0.28813
0.00..0.10: 986*************************************************
0.10..0.20:1043****************************************************
0.20..0.30: 992*************************************************
0.30..0.40: 974************************************************
0.40..0.50:1001**************************************************
0.50..0.60: 998*************************************************
0.60..0.70: 995*************************************************
0.70..0.80:1043****************************************************
0.80..0.90:1005**************************************************
0.90..1.00: 963************************************************
</pre>
For the extra credit, pretend we have a device that spews random numbers in the range [0..1) forever. We connect this device to a measuring device that calculates mean and std deviation, printing results on a regular basis.
<syntaxhighlight lang="zkl">var pipe=Thread.Pipe(); // used to connect the two threads
fcn{ while(1){ pipe.write((0.0).random(1.0)) } }.launch(); // generator
fcn{ // consumer/calculator
N:=0; M:=SD:=sum:=ssum:=0.0;
while(1){
x:=pipe.read(); N+=1; sum+=x; ssum+=x*x;
M=sum/N; SD=(ssum/N - M*M).sqrt();
if(0==N%100000)
println("N:%,10d mean:%.5f std dev:%.5f".fmt(N,M,SD));
}
}.launch();
Atomic.sleep(60*60); // wait because exiting the VM kills the threads</syntaxhighlight>
{{out}}
<pre>
...
N:45,800,000 mean:0.49997 std dev:0.28869
N:45,900,000 mean:0.49997 std dev:0.28869
N:46,000,000 mean:0.49997 std dev:0.28869
N:46,100,000 mean:0.49998 std dev:0.28869
N:46,200,000 mean:0.49997 std dev:0.28870
N:46,300,000 mean:0.49997 std dev:0.28870
N:46,400,000 mean:0.49997 std dev:0.28870
...
</pre>
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