Statistics/Basic
You are encouraged to solve this task according to the task description, using any language you may know.
Statistics is all about large groups of numbers. When talking about a set of sampled data, most frequently used is their mean value and standard deviation (stddev). If you have set of data where , the mean is , while the stddev is .
When examining a large quantity of data, one often uses a 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.)
- Hint
For a finite population with equal probabilities at all points, one can derive:
Or, more verbosely:
See also
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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)- Output:
## ## 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: ++++++++++++++++++++++++++++++++++++++++++++++++
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.
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- Output:
Screenshot from Atari 8-bit computer
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
Ada
A plain solution for moderate sample sizes
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;
- Output:
from a few sample runs
> ./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
Making the solution ready for one trillion samples
Depending on where you live, one trillion is either 10^12 or 10^18 [1]. 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
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;
- Output:
for sample size 10^12 took one night on my PC
................................................. 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
The same program should still work fine for sample size 10^18, but I'll need my PC in the meantime. ;-)
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).
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- Output:
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)
Amazing Hopper
#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
- Output:
$ 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 **************************************************
BASIC
Applesoft BASIC
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
Chipmunk Basic
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
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
- Output:
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 **************************************************
GW-BASIC
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
Liberty BASIC
Be aware that the PRNG in LB has a SLIGHT bias.
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- Output:
100000 data terms used. Mean =0.49870232 Stddev =0.28926563 ###################################################################### ###################################################################### ###################################################################### ###################################################################### ##################################################################### ##################################################################### ##################################################################### ##################################################################### ###################################################################### #####################################################################
MSX Basic
The GW-BASIC solution works without any changes.
PureBasic
Changes were made from the Liberty BASIC version to normalize the histogram as well as implement a random float function.
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
- Output:
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 ################################################################## ################################################################ ################################################################## #################################################################### ################################################################ ###################################################################### #################################################################### ################################################################### #################################################################### ####################################################################
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
Run BASIC
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 sub100 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 ******************************************************************
Yabasic
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
C
Sample code.
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdint.h>
#define n_bins 10
double rand01() { return rand() / (RAND_MAX + 1.0); }
double avg(int count, double *stddev, int *hist)
{
double x[count];
double m = 0, s = 0;
for (int i = 0; i < n_bins; i++) hist[i] = 0;
for (int i = 0; i < count; i++) {
m += (x[i] = rand01());
hist[(int)(x[i] * n_bins)] ++;
}
m /= count;
for (int i = 0; i < count; i++)
s += x[i] * x[i];
*stddev = sqrt(s / count - m * m);
return m;
}
void hist_plot(int *hist)
{
int max = 0, step = 1;
double inc = 1.0 / n_bins;
for (int i = 0; i < n_bins; i++)
if (hist[i] > max) max = hist[i];
/* scale if numbers are too big */
if (max >= 60) step = (max + 59) / 60;
for (int i = 0; i < n_bins; i++) {
printf("[%5.2g,%5.2g]%5d ", i * inc, (i + 1) * inc, hist[i]);
for (int j = 0; j < hist[i]; j += step)
printf("#");
printf("\n");
}
}
/* record for moving average and stddev. Values kept are sums and sum data^2
* to avoid excessive precision loss due to divisions, but some loss is inevitable
*/
typedef struct {
uint64_t size;
double sum, x2;
uint64_t hist[n_bins];
} moving_rec;
void moving_avg(moving_rec *rec, double *data, int count)
{
double sum = 0, x2 = 0;
/* not adding data directly to the sum in case both recorded sum and
* count of this batch are large; slightly less likely to lose precision*/
for (int i = 0; i < count; i++) {
sum += data[i];
x2 += data[i] * data[i];
rec->hist[(int)(data[i] * n_bins)]++;
}
rec->sum += sum;
rec->x2 += x2;
rec->size += count;
}
int main()
{
double m, stddev;
int hist[n_bins], samples = 10;
while (samples <= 10000) {
m = avg(samples, &stddev, hist);
printf("size %5d: %g %g\n", samples, m, stddev);
samples *= 10;
}
printf("\nHistograph:\n");
hist_plot(hist);
printf("\nMoving average:\n N Mean Sigma\n");
moving_rec rec = { 0, 0, 0, {0} };
double data[100];
for (int i = 0; i < 10000; i++) {
for (int j = 0; j < 100; j++) data[j] = rand01();
moving_avg(&rec, data, 100);
if ((i % 1000) == 999) {
printf("%4lluk %f %f\n",
rec.size/1000,
rec.sum / rec.size,
sqrt(rec.x2 * rec.size - rec.sum * rec.sum)/rec.size
);
}
}
}
C#
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);
}
}
- Output:
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
C++
#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 ;
}
- Output:
./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 !
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
- Output:
> 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
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;
}
}
}
Compile with "-version=statistics_basic_main" to run the main function.
- Output:
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: *************************************************
Dart
/* 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('');
}
}
- Output:
--------------- 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
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 100000Elixir
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)
- Output:
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:=================================================
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
- Output:
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
Fortran
This version will handle numbers as large as 1 trillion or more if you are prepared to wait long enough
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
- Output:
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: =================================================
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()
}
- Output:
100 numbers Mean: 0.5231064889267764 Stddev: 0.292668237816841 **************** **************** ************************ ********************** ****************** ****************** **************** ************************** ************************ ******************** 1000 numbers Mean: 0.496026080160094 Stddev: 0.2880988956436907 ********************* ******************** ***************** *********************** ****************** ********************** ******************** ********************* ****************** ******************* 10000 numbers Mean: 0.5009091903581223 Stddev: 0.289269693719711 ******************* ******************** ******************** ******************** ********************* ******************** ******************* ******************* ******************** *********************
The usual approach to the extra problem is 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 threshold in the code below to optimize cache performance.
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
}
- Output:
10000000 numbers Mean: 0.4999673191148989 Stddev: 0.2886663876567514 ******************** ******************** ******************** ******************** ******************** ******************** ******************** ******************** ******************** ********************
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'
- Output:
./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: ***************************************************
Hy
(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)
Icon and Unicon
The following uses the stddev procedure from the Standard_deviation task. In this example,
- Output:
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 : *************************************************
J
J has library routines to compute mean and standard deviation:
require 'stats'
(mean,stddev) 1000 ?@$ 0
0.484669 0.287482
(mean,stddev) 10000 ?@$ 0
0.503642 0.290777
(mean,stddev) 100000 ?@$ 0
0.499677 0.288726
And, for a histogram:
histogram=: <: @ (#/.~) @ (i.@#@[ , I.)
require'plot'
plot ((% * 1 + i.)100) ([;histogram) 10000 ?@$ 0
but these are not quite what is being asked for here.
Instead:
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.
data=. (chunk|y) ?@$ 0
h=. h+ bins histogram data
s=. s+ +/ data
t=. t+ +/ *: data - 0.5
smoutput (<.300*h%y) #"0 '#'
(s%y) , %:t%y
)
Example use:
meanstddevP 1000
#############################
####################################
###########################
##############################
###################################
########################
###########################
############################
################################
##########################
0.488441 0.289744
meanstddevP 10000
##############################
##############################
#############################
#############################
###############################
##############################
############################
##############################
#############################
#############################
0.49697 0.289433
meanstddevP 100000
#############################
##############################
#############################
#############################
#############################
##############################
##############################
##############################
##############################
#############################
0.500872 0.288241
(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.
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);
}
}
}
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: **************************************************
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:
# Usage: prng N width
function prng {
cat /dev/urandom | tr -cd '0-9' | fold -w "$2" | head -n "$1"
}
basicStats.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)] )Driver Script (e.g. bash)
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
- Output:
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 : ********************
Jsish
#!/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!=
*/
- Output:
prompt$ jsish -u statisticsBasic.jsi [PASS] statisticsBasic.jsi
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
- Output:
## ## 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: +++++++++++++++++++++++++++++++++++++++++++++++++
Klong
Using the "mu" (mean) and "sd" (standard deviation) functions from the Klong statistics library:
.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)
- Output:
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
Kotlin
// 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)
}
Sample run:
- Output:
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 **************************************************
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'
^}
- Output:
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: ++++++++++++++++++++++++
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.
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
Maple
The following samples 100 uniformly distributed numbers between 0 and 1:
with(Statistics):
X_100 := Sample( Uniform(0,1), 100 );
Mean( X_100 );
StandardDeviation( X_100 );
Histogram( X_100 );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:
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 );Mathematica /Wolfram Language
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}
- Output:
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
MATLAB / Octave
% 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)
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).
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
- Output:
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: ===================
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 RunningStat. 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).
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()
- Output:
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
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
] ;- Output:
>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 >
PARI/GP
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);For versions before 2.4.3, define
rreal()={
my(pr=32*ceil(default(realprecision)*log(10)/log(4294967296))); \\ Current precision
random(2^pr)*1.>>pr
};and use rreal() in place of random(1.).
PascalABC.NET
procedure hist(numbers: array of real);
begin
var h := arrfill(10, 0);
foreach var n in numbers do h[floor(10 * n)] += 1;
for var i := 0 to 9 do
Writeln(i / 10:1:1, '+ ', '+' * floor(h[i] / h.Max * 50));
end;
begin
foreach var n in |100, 1_000, 10_000, 1_000_000| do
begin
var numbers := ArrRandomReal(n, 0, 1, 10);
var mean := numbers.Average;
var std := numbers.Sum(x -> Sqr(x - mean) / n).Sqrt;
println('numbers:', n, 'mean:', mean, 'stddev:', std);
hist(numbers);
Println;
end;
end.
- Output:
numbers: 100 mean: 0.52545755072 stddev: 0.278457054172447 0.0+ ++++++++++++++++++++++++++ 0.1+ ++++++++++++++++++++++++++++++ 0.2+ ++++++++++++++++++++++++++++++++++++ 0.3+ ++++++++++++++++++++++++++ 0.4+ +++++++++++++++++++++++ 0.5+ ++++++++++++++++++++++++++++++++++++++++++++++ 0.6+ ++++++++++++++++++++++++++ 0.7+ ++++++++++++++++++++++++++++++++++++++++++++++++++ 0.8+ ++++++++++++++++++++++++++++++++++++++++ 0.9+ ++++++++++++++++++++++++++ numbers: 1000 mean: 0.499691152139801 stddev: 0.283110050785109 0.0+ ++++++++++++++++++++++++++++++++++++++++ 0.1+ +++++++++++++++++++++++++++++++++++++++++++++ 0.2+ ++++++++++++++++++++++++++++++++++++++++++++++++ 0.3+ +++++++++++++++++++++++++++++++++++++++++++++ 0.4+ +++++++++++++++++++++++++++++++++++++++++++++ 0.5+ ++++++++++++++++++++++++++++++++++++++++++++++++++ 0.6+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.7+ +++++++++++++++++++++++++++++++++++++++++ 0.8+ +++++++++++++++++++++++++++++++++++++++++ 0.9+ ++++++++++++++++++++++++++++++++++++++++++++++ numbers: 10000 mean: 0.497660862386219 stddev: 0.288880727467724 0.0+ ++++++++++++++++++++++++++++++++++++++++++++++++++ 0.1+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.2+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.3+ +++++++++++++++++++++++++++++++++++++++++++++++ 0.4+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.5+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.6+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.7+ +++++++++++++++++++++++++++++++++++++++++++++++ 0.8+ ++++++++++++++++++++++++++++++++++++++++++++++ 0.9+ +++++++++++++++++++++++++++++++++++++++++++++++++ numbers: 1000000 mean: 0.500252110481309 stddev: 0.288709683877751 0.0+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.1+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.2+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.3+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.4+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.5+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.6+ ++++++++++++++++++++++++++++++++++++++++++++++++++ 0.7+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.8+ +++++++++++++++++++++++++++++++++++++++++++++++++ 0.9+ +++++++++++++++++++++++++++++++++++++++++++++++++
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";
}
Usage:
perl rand_statistics.pl (number of values)
$ 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 : *******************************
Phix
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.
function generate_statistics(integer n) sequence hist = repeat(0,10) atom sum_r = 0, sum_squares = 0.0 for i=1 to n do atom r = rnd() sum_r += r sum_squares += r*r hist[floor(10*r)+1] += 1 end for atom mean = sum_r / n atom stddev = sqrt((sum_squares / n) - mean*mean) return {n, mean, stddev, hist} end function procedure display_statistics(sequence x) atom n, mean, stddev sequence hist {n, mean, stddev, hist} = x printf(1,"-- Stats for sample size %d\n",{n}) printf(1,"mean: %g\n",{mean}) printf(1,"sdev: %g\n",{stddev}) for i=1 to length(hist) do integer cnt = hist[i] string bars = repeat('=',floor(cnt*300/n)) printf(1,"%.1f: %s %d\n",{i/10,bars,cnt}) end for end procedure for n=2 to 5 do display_statistics(generate_statistics(power(10,n+(n=5)))) end for
- Output:
-- 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
-- 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
-- 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
-- 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
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.
(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) )- Output:
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 ========================================
PL/I
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;- Output:
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
Python
The second function, sd2 only needs to go once through the numbers and so can more efficiently handle large streams of numbers.
def sd1(numbers):
if numbers:
mean = sum(numbers) / len(numbers)
sd = (sum((n - mean)**2 for n in numbers) / len(numbers))**0.5
return sd, mean
else:
return 0, 0
def sd2(numbers):
if numbers:
sx = sxx = n = 0
for x in numbers:
sx += x
sxx += x*x
n += 1
sd = (n * sxx - sx*sx)**0.5 / n
return sd, sx / n
else:
return 0, 0
def histogram(numbers):
h = [0] * 10
maxwidth = 50 # characters
for n in numbers:
h[int(n*10)] += 1
mx = max(h)
print()
for n, i in enumerate(h):
print('%3.1f: %s' % (n / 10, '+' * int(i / mx * maxwidth)))
print()
if __name__ == '__main__':
import random
for i in range(1, 6):
n = [random.random() for j in range(10**i)]
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)
- Output:
for larger sets of random numbers, the distribution of numbers between the bins of the histogram evens out.
... ## ## 100 numbers ## Naive method: sd: 0.288911, mean: 0.508686 Second method: sd: 0.288911, mean: 0.508686 0.0: +++++++++++++++++++++++++++++++ 0.1: ++++++++++++++++++++++++++++ 0.2: +++++++++++++++++++++++++ 0.3: ++++++++++++++++++++++++++++++++++++++++++++++++++ 0.4: ++++++++++++++++++ 0.5: +++++++++++++++++++++++++++++++ 0.6: ++++++++++++++++++ 0.7: +++++++++++++++++++++++++++++++++++++ 0.8: ++++++++++++++++++++++++++++++++++++++++ 0.9: +++++++++++++++++++++++++++++++ ... ## ## 10000000 numbers ## Naive method: sd: 0.288750, mean: 0.499839 Second method: sd: 0.288750, mean: 0.499839 0.0: ++++++++++++++++++++++++++++++++++++++++++++++++++ 0.1: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.2: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.3: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.4: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.5: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.6: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.7: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.8: +++++++++++++++++++++++++++++++++++++++++++++++++ 0.9: +++++++++++++++++++++++++++++++++++++++++++++++++
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.
#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)))
Output
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
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)
- Output:
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: *******************
Raku
(formerly Perl 6)
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 '';
}
- Output:
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 ==================================================
REXX
Twenty decimal digits are used for the calculations, but only half that (ten digits) are displayed in the output.
/*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
- output when using the default input of: 100
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
- output when using the default input of: 1000
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
- output when using the default input of: 10000
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
- output when using the default input of: 100000
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
- output when using the default input of: 1000000
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
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 nlOutput:
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 *********************************************************************
RPL
Built-in statistics functions in RPL relies on a specific array named ∑DAT, which is automatically generated when the first record is created by the word ∑+.
| 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
≫ ≫ ‘TASK’ STO
|
TASK ( #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 TASK
- Output:
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= *****************" }
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}
- Output:
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:=================================================================
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);
}
}
- Output:
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: ***************************************
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
}
- Output:
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
Sidef
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) }
- Output:
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:====================================================================
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.
. 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
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
- Output:
100 numbers Mean: 0.4801193240797704 StdDev: 0.28697057708153784 ************** ********************************** ******************** ************** **************************** **************** ************** **************************** **************** **************** 1000 numbers Mean: 0.49478823525495275 StdDev: 0.2821543810265757 ******************* ****************** ************************ ******************** ******************* ********************** ********************* ******************** ****************** ****************** 10000 numbers Mean: 0.49928563715870816 StdDev: 0.2888258479070212 ******************** ********************* ******************** ******************** ******************* ********************* ******************* ******************** ********************* ********************
As can be seen, increasing the sample size reduces the variation between the buckets, showing that the rand() 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.)
VBA
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$(t(i, 1) / (10 ^ (e - 2)), "X");
Debug.Print
Next i
Debug.Print
Next e
End Sub
- Output:
sample size 100 mean 0,472405961751938 standard deviation 0,260463885857138 0,00-0,10 XXXXXX 0,10-0,20 XXXXXXXXX 0,20-0,30 XXXXXXXXXXXXXXX 0,30-0,40 XXXXXXXXXXXXXXX 0,40-0,50 XXXXXXXXXXXXXX 0,50-0,60 XXXXXXX 0,60-0,70 XXXXXXXXXXX 0,70-0,80 XXXXXXXX 0,80-0,90 XXXXXXXXXX 0,90-1,00 XXXXX sample size 1000 mean 0,500459910154343 standard deviation 0,278991757028358 0,00-0,10 XXXXXXXX 0,10-0,20 XXXXXXXXXX 0,20-0,30 XXXXXXXXXX 0,30-0,40 XXXXXXXXXX 0,40-0,50 XXXXXXXXXX 0,50-0,60 XXXXXXXXXXXX 0,60-0,70 XXXXXXXXXXX 0,70-0,80 XXXXXXXXX 0,80-0,90 XXXXXXXXX 0,90-1,00 XXXXXXXXXX sample size 10000 mean 0,496753623914719 standard deviation 0,28740805585887 0,00-0,10 XXXXXXXXXX 0,10-0,20 XXXXXXXXXX 0,20-0,30 XXXXXXXXXX 0,30-0,40 XXXXXXXXXX 0,40-0,50 XXXXXXXXXX 0,50-0,60 XXXXXXXXXX 0,60-0,70 XXXXXXXXXX 0,70-0,80 XXXXXXXXXX 0,80-0,90 XXXXXXXXXX 0,90-1,00 XXXXXXXXXX
V (Vlang)
import rand
import math
fn main() {
sample(100)
sample(1000)
sample(10000)
}
fn sample(n int) {
// generate data
mut d := []f64{len: n}
for i in 0.. d.len {
d[i] = rand.f64()
}
// show mean, standard deviation
mut sum, mut ssq := f64(0), f64(0)
for s in d {
sum += s
ssq += s * s
}
println("$n numbers")
m := sum / f64(n)
println("Mean: $m")
println("Stddev: ${math.sqrt(ssq/f64(n)-m*m)}")
// show histogram
mut h := []int{len: 10}
for s in d {
h[int(s*10)]++
}
for c in h {
println("*".repeat(c*205/int(n)))
}
println('')
}- Output:
Sample run:
100 numbers Mean: 0.4673526451482236 Stddev: 0.27590441169077806 **************** ******************************** ******************** ******************** ************ ****************************** ************ ********************************** ********** ************** 1000 numbers Mean: 0.4906097518067266 Stddev: 0.28686496927912264 ******************** ********************* ********************** ********************* ******************** ***************** ******************* ********************* ******************** ****************** 10000 numbers Mean: 0.5012521647492316 Stddev: 0.2883488134311142 ******************** ******************** ********************* ****************** ********************* ********************* ******************** ******************** ******************** ********************
Or use standard math.stats module
import rand
import math.stats
fn main() {
sample(100)
sample(1000)
sample(10000)
}
fn sample(n int) {
// generate data
mut d := []f64{len: n}
for i in 0.. d.len {
d[i] = rand.f64()
}
// show mean, standard deviation
println("$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('')
}
- Output:
Similar to above
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")
}
- Output:
Sample run:
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: **********
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;
]- Output:
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: **********
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()
}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)));
}(0.0).random(1.0) generates a [uniform] random number between 0 (inclusive) and 1 (exclusive).
- Output:
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************************************************
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.
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- Output:
... 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 ...
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