# Statistics/Basic

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 ${\displaystyle x_{i}}$ where ${\displaystyle i=1,2,\ldots ,n\,\!}$, the mean is ${\displaystyle {\bar {x}}\equiv {1 \over n}\sum _{i}x_{i}}$, while the stddev is ${\displaystyle \sigma \equiv {\sqrt {{1 \over n}\sum _{i}\left(x_{i}-{\bar {x}}\right)^{2}}}}$.

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:

${\displaystyle {\overline {(x-{\overline {x}})^{2}}}={\overline {x^{2}}}-{\overline {x}}^{2}}$

Or, more verbosely:

${\displaystyle {\frac {1}{N}}\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}={\frac {1}{N}}\left(\sum _{i=1}^{N}x_{i}^{2}\right)-{\overline {x}}^{2}.}$

## 11l

Translation of: Python
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)
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)
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:
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

### A plain solution for moderate sample sizes

with Ada.Text_IO, Ada.Command_Line, Ada.Numerics.Float_Random,

procedure Basic_Stat is

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
end loop;
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);
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;

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,

procedure Long_Basic_Stat is

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
end loop;
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);
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;

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
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 # ;

# 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:
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 */
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:
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

Works with: Chipmunk Basic
Works with: GW-BASIC
Works with: MSX BASIC
Translation of: Chipmunk 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

Works with: Chipmunk Basic version 3.6.4
Works with: QBasic
Translation of: Yabasic
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
For i As Integer = 0 To 9
If h(i) >= 0 Then Exit For
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

Works with: Applesoft BASIC
Works with: Chipmunk Basic
Works with: PC-BASIC version any
Works with: MSX BASIC
Translation of: Chipmunk 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

Translation of: Liberty BASIC

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

Works with: QBasic version 1.1
Works with: QuickBasic version 4.5
Translation of: Yabasic
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 sub
100 Samples used.
Mean    = 0.514312738
Std Dev = 0.291627558
0 **************************************************************************************************
1 **********************************************************************
2 *********************
3 ***********************************
4 ***************************************************************
5 *******************************************************************************************
6 ***********************************************************************************************************************
7 **********************************************************************
8 ***************************************************************
9 **********************************************************************

1000 Samples used.
Mean    = 0.495704208
Std Dev = 0.281389168
0 ***************************************************************
1 ********************************************************************
2 **************************************************************************
3 *******************************************************************************
4 **************************************************************************
5 **********************************************************************
6 ************************************************************************
7 **********************************************************************
8 ********************************************************
9 **********************************************************************

10000 Samples used.
Mean    = 0.493594211
Std Dev = 0.288635912
0 ************************************************************************
1 ************************************************************************
2 **********************************************************************
3 *******************************************************************
4 **********************************************************************
5 ************************************************************************
6 ************************************************************************
7 *****************************************************************
8 **********************************************************************
9 ******************************************************************

### Yabasic

Translation of: Run BASIC
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#

Library: Math.Net
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

Translation of: Python
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 v & " " & s$. . numfmt 4 5 proc stats size . . mklist size print "Size: " & size print "Mean: " & mean print "Stddev: " & stddev histo print "" . stats 100 stats 1000 stats 10000 stats 100000 ## Elixir Translation of: Ruby 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

Works with: Fortran version 95 and later

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
********************
********************
********************
********************
********************
********************
********************
********************
********************
********************


import Data.Foldable (foldl') --'
import System.Random (randomRs, newStdGen)
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, procedure main(A) W := 50 # avg width for histogram bar B := 10 # histogram bins if *A = 0 then put(A,100) # 100 if none specified while N := get(A) do { # once per argument write("\nN=",N) N := 0 < integer(N) | next # skip if invalid stddev() # reset m := 0. H := list(B,0) # Histogram of every i := 1 to N do { # calc running ... s := stddev(r := ?0) # ... std dev m +:= r/N # ... mean H[integer(*H*r)+1] +:= 1 # ... histogram } write("mean=",m) write("stddev=",s) every i := 1 to *H do # show histogram write(right(real(i)/*H,5)," : ",repl("*",integer(*H*50./N*H[i]))) } end  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 Translation of Python via D Works with: Java version 8 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: 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   = ",$sd(s))} plot(100) plot(1000) plot(10000)  Output: n = 100 0.0 ***************** 0.1 ****** 0.2 ******** 0.3 ********** 0.4 *********** 0.5 ********* 0.6 *********** 0.7 ********** 0.8 ****** 0.9 ************ mean = 0.482634518758 sd = 0.300804579739938409 n = 1000 0.0 ******* 0.1 ******** 0.2 *********** 0.3 *********** 0.4 ********* 0.5 *********** 0.6 ******** 0.7 ************ 0.8 ********** 0.9 ******** mean = 0.510119356421 sd = 0.277396945925369919 n = 10000 0.0 ********** 0.1 ********* 0.2 ********* 0.3 ********** 0.4 ********* 0.5 ********** 0.6 ********* 0.7 ********* 0.8 ********** 0.9 ********** mean = 0.49854591894824 sd = 0.290375399458904972  ## Kotlin Translation of: FreeBASIC // version 1.1.2 val rand = java.util.Random() fun basicStats(sampleSize: Int) { if (sampleSize < 1) return val r = DoubleArray(sampleSize) val h = IntArray(10) // all zero by default /* Generate 'sampleSize' random numbers in the interval [0, 1) and calculate in which box they will fall when drawing the histogram */ for (i in 0 until sampleSize) { r[i] = rand.nextDouble() h[(r[i] * 10).toInt()]++ } // adjust one of the h[] values if necessary to ensure they sum to sampleSize val adj = sampleSize - h.sum() if (adj != 0) { for (i in 0..9) { h[i] += adj if (h[i] >= 0) break h[i] -= adj } } val mean = r.average() val sd = Math.sqrt(r.map { (it - mean) * (it - mean) }.average()) // Draw a histogram of the data with interval 0.1 var numStars: Int // If sample size > 500 then normalize histogram to 500 val scale = if (sampleSize <= 500) 1.0 else 500.0 / sampleSize println("Sample size$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)
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

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)
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

Works with: PARI/GP version 2.4.3 and above
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.).

## 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 Translation of: CoffeeScript To do a trillion samples, I would change the existing generate loop into an inner 100_000_000 loop that still uses the fast native types, with everything outside that changed to bigatom, and of course add an outer loop which sums into them. 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) Works with: rakudo version 2018.03 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 nl Output: 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 ∑+. Works with: Halcyon Calc version 4.2.8 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 Library: rand #![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 Translation of: Ruby func generate_statistics(n) { var(sum=0, sum2=0) var hist = 10.of(0) n.times { var r = 1.rand sum += r sum2 += r**2 hist[10*r] += 1 } var mean = sum/n var stddev = sqrt(sum2/n - mean**2) say "size: #{n}" say "mean: #{mean}" say "stddev: #{stddev}" var max = hist.max for i in ^hist { printf("%.1f:%s\n", 0.1*i, "=" * 70*hist[i]/max) } print "\n" } [100, 1000, 10000].each {|n| generate_statistics(n) }  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)

Translation of: go
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

Library: Wren-math
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

Translation of: Wren
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){
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
...