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Statistics/Basic

From Rosetta Code
Task
Statistics/Basic
You are encouraged to solve this task according to the task description, using any language you may know.

Statistics is all about large groups of numbers. When talking about a set of sampled data, most frequently used is their mean value and standard deviation (stddev). If you have set of data where , the mean is , while the stddev is .

When examining a large quantity of data, one often uses a histogram, which shows the counts of data samples falling into a prechosen set of intervals (or bins). When plotted, often as bar graphs, it visually indicates how often each data value occurs.

Task Using your language's random number routine, generate real numbers in the range of [0, 1]. It doesn't matter if you chose to use open or closed range. Create 100 of such numbers (i.e. sample size 100) and calculate their mean and stddev. Do so for sample size of 1,000 and 10,000, maybe even higher if you feel like. Show a histogram of any of these sets. Do you notice some patterns about the standard deviation?

Extra Sometimes so much data need to be processed that it's impossible to keep all of them at once. Can you calculate the mean, stddev and histogram of a trillion numbers? (You don't really need to do a trillion numbers, just show how it can be done.)

Hint

For a finite population with equal probabilities at all points, one can derive:

Or, more verbosely:

See also


Ada[edit]

A plain solution for moderate sample sizes[edit]

with Ada.Text_IO, Ada.Command_Line, Ada.Numerics.Float_Random,
Ada.Numerics.Generic_Elementary_Functions;
 
procedure Basic_Stat is
 
package FRG renames Ada.Numerics.Float_Random;
package TIO renames Ada.Text_IO;
 
type Counter is range 0 .. 2**31-1;
type Result_Array is array(Natural range <>) of Counter;
 
package FIO is new TIO.Float_IO(Float);
 
procedure Put_Histogram(R: Result_Array; Scale, Full: Counter) is
begin
for I in R'Range loop
FIO.Put(Float'Max(0.0, Float(I)/10.0 - 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put("..");
FIO.Put(Float'Min(1.0, Float(I)/10.0 + 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put(": ");
for J in 1 .. (R(I)* Scale)/Full loop
Ada.Text_IO.Put("X");
end loop;
Ada.Text_IO.New_Line;
end loop;
end Put_Histogram;
 
procedure Put_Mean_Et_Al(Sample_Size: Counter;
Val_Sum, Square_Sum: Float) is
Mean: constant Float := Val_Sum / Float(Sample_Size);
package Math is new Ada.Numerics.Generic_Elementary_Functions(Float);
begin
TIO.Put("Mean: ");
FIO.Put(Mean, Fore => 1, Aft => 5, Exp => 0);
TIO.Put(", Standard Deviation: ");
FIO.Put(Math.Sqrt(abs(Square_Sum / Float(Sample_Size)
- (Mean * Mean))), Fore => 1, Aft => 5, Exp => 0);
TIO.New_Line;
end Put_Mean_Et_Al;
 
N: Counter := Counter'Value(Ada.Command_Line.Argument(1));
Gen: FRG.Generator;
Results: Result_Array(0 .. 10) := (others => 0);
X: Float;
Val_Sum, Squ_Sum: Float := 0.0;
 
begin
FRG.Reset(Gen);
for I in 1 .. N loop
X := FRG.Random(Gen);
Val_Sum  := Val_Sum + X;
Squ_Sum := Squ_Sum + X*X;
declare
Index: Integer := Integer(X*10.0);
begin
Results(Index) := Results(Index) + 1;
end;
end loop;
TIO.Put_Line("After sampling" & Counter'Image(N) & " random numnbers: ");
Put_Histogram(Results, Scale => 600, Full => N);
TIO.New_Line;
Put_Mean_Et_Al(Sample_Size => N, Val_Sum => Val_Sum, Square_Sum => Squ_Sum);
end Basic_Stat;
Output:
from a few sample runs:
> ./basic_stat 1000
After sampling 1000 random numnbers: 
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXX

Mean: 0.48727,  Standard Deviation: 0.28502



> ./basic_stat 10_000
After sampling 10000 random numnbers: 
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Mean: 0.50096,  Standard Deviation: 0.28869



> ./basic_stat 100_000
After sampling 100000 random numnbers: 
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Mean: 0.50178,  Standard Deviation: 0.28805

Making the solution ready for one trillion samples[edit]

Depending on where you live, one trillion is either 10^12 or 10^18 [1]. Below, I'll assume 10^12, which implies a number of operations I can still perform on my PC.

The above program will fail with such large inputs for two reasons:

1. The type Counter cannot hold such large numbers.

2. The variables Val_Sum and Squ_Sum will numerically fail, because the type Float only provides about six decimal digits of accuracy. I.e., at some point, Val_Sum and (a little bit later) Squ_Sum are so large that adding a value below 1 has no effect, any more.

To make the program ready for sample size 10^12, we modify it as follows.

1. Change the type Counter to hold such large numbers.

2. Define a type High_Precision, that will hold (at least) 15 decimal digits. Define Val_Sum and Squ_Sum as being from that type. Include the neccessary type conversions.

3. Provide some progress report, during the running time.

This is the modified program

with Ada.Text_IO, Ada.Command_Line, Ada.Numerics.Float_Random,
Ada.Numerics.Generic_Elementary_Functions;
 
procedure Long_Basic_Stat is
 
package FRG renames Ada.Numerics.Float_Random;
package TIO renames Ada.Text_IO;
 
type Counter is range 0 .. 2**63-1;
type Result_Array is array(Natural range <>) of Counter;
type High_Precision is digits 15;
 
package FIO is new TIO.Float_IO(Float);
 
procedure Put_Histogram(R: Result_Array; Scale, Full: Counter) is
begin
for I in R'Range loop
FIO.Put(Float'Max(0.0, Float(I)/10.0 - 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put("..");
FIO.Put(Float'Min(1.0, Float(I)/10.0 + 0.05),
Fore => 1, Aft => 2, Exp => 0); TIO.Put(": ");
for J in 1 .. (R(I)* Scale)/Full loop
Ada.Text_IO.Put("X");
end loop;
Ada.Text_IO.New_Line;
end loop;
end Put_Histogram;
 
procedure Put_Mean_Et_Al(Sample_Size: Counter;
Val_Sum, Square_Sum: Float) is
Mean: constant Float := Val_Sum / Float(Sample_Size);
package Math is new Ada.Numerics.Generic_Elementary_Functions(Float);
begin
TIO.Put("Mean: ");
FIO.Put(Mean, Fore => 1, Aft => 5, Exp => 0);
TIO.Put(", Standard Deviation: ");
FIO.Put(Math.Sqrt(abs(Square_Sum / Float(Sample_Size)
- (Mean * Mean))), Fore => 1, Aft => 5, Exp => 0);
TIO.New_Line;
end Put_Mean_Et_Al;
 
N: Counter := Counter'Value(Ada.Command_Line.Argument(1));
Gen: FRG.Generator;
Results: Result_Array(0 .. 10) := (others => 0);
X: Float;
Val_Sum, Squ_Sum: High_Precision := 0.0;
 
begin
FRG.Reset(Gen);
for Outer in 1 .. 1000 loop
for I in 1 .. N/1000 loop
X := FRG.Random(Gen);
Val_Sum  := Val_Sum + High_Precision(X);
Squ_Sum := Squ_Sum + High_Precision(X)*High_Precision(X);
declare
Index: Integer := Integer(X*10.0);
begin
Results(Index) := Results(Index) + 1;
end;
end loop;
if Outer mod 50 = 0 then
TIO.New_Line(1);
TIO.Put_Line(Integer'Image(Outer/10) &"% done; current results:");
Put_Mean_Et_Al(Sample_Size => (Counter(Outer)*N)/1000,
Val_Sum => Float(Val_Sum),
Square_Sum => Float(Squ_Sum));
else
Ada.Text_IO.Put(".");
end if;
end loop;
TIO.New_Line(4);
TIO.Put_Line("After sampling" & Counter'Image(N) & " random numnbers: ");
Put_Histogram(Results, Scale => 600, Full => N);
TIO.New_Line;
Put_Mean_Et_Al(Sample_Size => N,
Val_Sum => Float(Val_Sum), Square_Sum => Float(Squ_Sum));
end Long_Basic_Stat;
Output:
for sample size 10^12 took one night on my PC:
.................................................
 5% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28867
.................................................
 10% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28867
.................................................
 15% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 20% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 25% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 30% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 35% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 40% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 45% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 50% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 55% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 60% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 65% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 70% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 75% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 80% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 85% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 90% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 95% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868
.................................................
 100% done; current results:
Mean: 0.50000,  Standard Deviation: 0.28868




After sampling 1000000000000 random numnbers: 
0.00..0.05: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.05..0.15: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.15..0.25: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.25..0.35: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.35..0.45: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.45..0.55: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.55..0.65: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.65..0.75: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.75..0.85: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.85..0.95: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0.95..1.00: XXXXXXXXXXXXXXXXXXXXXXXXXXXXXX

Mean: 0.50000,  Standard Deviation: 0.28868

The same program should still work fine for sample size 10^18, but I'll need my PC in the meantime. ;-)

C[edit]

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#[edit]

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++[edit]

#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[edit]

 
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[edit]

Translation of: Python
import std.stdio, std.algorithm, std.array, std.typecons,
std.range, std.exception;
 
auto meanStdDev(R)(R numbers) /*nothrow*/ @safe [email protected]*/ {
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) [email protected]*/ {
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[edit]

/* Import math library to get:
* 1) Square root function  : Math.sqrt(x)
* 2) Power function : Math.pow(base, exponent)
* 3) Random number generator : Math.Random()
*/

import 'dart:math' as Math show sqrt, pow, Random;
 
// Returns average/mean of a list of numbers
num mean(List<num> l) => l.reduce((num value,num element)=>value+element)/l.length;
 
// Returns standard deviation of a list of numbers
num stdev(List<num> l) => Math.sqrt((1/l.length)*l.map((num x)=>x*x).reduce((num value,num element) => value+element) - Math.pow(mean(l),2));
 
/* CODE TO PRINT THE HISTOGRAM STARTS HERE
*
* Histogram has ten fields, one for every tenth between 0 and 1
* To do this, we save the histogram as a global variable
* that will hold the number of occurences of each tenth in the sample
*/

List<num> histogram = new List.filled(10,0);
 
/*
* METHOD TO CREATE A RANDOM SAMPLE OF n NUMBERS (Returns a list)
*
* While creating each value, this method also increments the
* appropriate index of the histogram
*/

List<num> randomsample(num n){
List<num> l = new List<num>(n);
histogram = new List.filled(10,0);
num random = new Math.Random();
for (int i = 0; i < n; i++){
l[i] = random.nextDouble();
histogram[conv(l[i])] += 1;
}
return l;
}
 
/*
* METHOD TO RETURN A STRING OF n ASTERIXES (yay ASCII art)
*/

String stars(num n){
String s = '';
for (int i = 0; i < n; i++){
s = s + '*';
}
return s;
}
 
/*
* METHOD TO DRAW THE HISTOGRAM
* 1) Get to total for all the values in the histogram
* 2) For every field in the histogram:
* a) Compute the frequency for every field in the histogram
* b) Print the frequency as asterixes
*/

void drawhistogram(){
int total = histogram.reduce((num element,num value)=>element+value);
double freq;
for (int i = 0; i < 10; i++){
freq = histogram[i]/total;
print('${i/10} - ${(i+1)/10} : ' + stars(conv(30*freq)));
}
}
 
/* HELPER METHOD:
* converts values between 0-1 to integers between 0-9 inclusive
* useful to figure out which random value generated
* corresponds to which field in the histogram
*/

int conv(num i) => (10*i).floor();
 
 
/* MAIN FUNCTION
*
* Create 5 histograms and print the mean and standard deviation for each:
* 1) Sample Size = 100
* 2) Sample Size = 1000
* 3) Sample Size = 10000
* 4) Sample Size = 100000
* 5) Sample Size = 1000000
*
*/

void main(){
List<num> l;
num m;
num s;
List<int> sampleSizes = [100,1000,10000,100000,1000000];
for (int samplesize in sampleSizes){
print('--------------- Sample size $samplesize ----------------');
l = randomsample(samplesize);
m = mean(l);
s = stdev(l);
drawhistogram();
print('');
print('mean: ${m.toStringAsPrecision(8)} standard deviation: ${s.toStringAsPrecision(8)}');
print('');
}
}
Output:
---------------  Sample size 100   ----------------
0.0 - 0.1 : ******************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : **************************
0.3 - 0.4 : **************************
0.4 - 0.5 : ***************************************
0.5 - 0.6 : *********************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : *********************************
0.8 - 0.9 : ************************
0.9 - 1.0 : **************************

mean: 0.49246975   standard deviation: 0.27789056

---------------  Sample size 1000   ----------------
0.0 - 0.1 : *************************
0.1 - 0.2 : *************************
0.2 - 0.3 : ******************************
0.3 - 0.4 : *******************************
0.4 - 0.5 : *********************************
0.5 - 0.6 : **********************************
0.6 - 0.7 : ********************************
0.7 - 0.8 : ****************************
0.8 - 0.9 : ****************************
0.9 - 1.0 : *******************************

mean: 0.51170283   standard deviation: 0.28170178

--------------   Sample size 10000   ----------------
0.0 - 0.1 : *****************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : ****************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : *****************************
0.5 - 0.6 : ******************************
0.6 - 0.7 : *******************************
0.7 - 0.8 : ******************************
0.8 - 0.9 : ******************************
0.9 - 1.0 : *******************************

mean: 0.50517609  standard deviation: 0.28923152

--------------   Sample size 100000  ----------------
0.0 - 0.1 : ******************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : *****************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : *****************************
0.5 - 0.6 : ******************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : *****************************
0.8 - 0.9 : *****************************
0.9 - 1.0 : ******************************

mean: 0.49994544   standard deviation: 0.28879394

--------------  Sample size 1000000  ----------------
0.0 - 0.1 : *****************************
0.1 - 0.2 : ******************************
0.2 - 0.3 : *****************************
0.3 - 0.4 : *****************************
0.4 - 0.5 : ******************************
0.5 - 0.6 : *****************************
0.6 - 0.7 : ******************************
0.7 - 0.8 : *****************************
0.8 - 0.9 : *****************************
0.9 - 1.0 : ******************************

mean: 0.50013331   standard deviation: 0.28864180

Elixir[edit]

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:=================================================

Fortran[edit]

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: =================================================

FreeBASIC[edit]

' FB 1.05.0 Win64
 
Randomize
 
Sub basicStats(sampleSize As Integer)
If sampleSize < 1 Then Return
Dim r(1 To sampleSize) As Double
Dim h(0 To 9) As Integer '' all zero by default
Dim sum As Double = 0.0
Dim hSum As Integer = 0
 
' Generate 'sampleSize' random numbers in the interval [0, 1)
' calculate their sum
' and in which box they will fall when drawing the histogram
For i As Integer = 1 To sampleSize
r(i) = Rnd
sum += r(i)
h(Int(r(i) * 10)) += 1
Next
 
For i As Integer = 0 To 9 : hSum += h(i) : Next
' adjust one of the h() values if necessary to ensure hSum = sampleSize
Dim adj As Integer = sampleSize - hSum
If adj <> 0 Then
For i As Integer = 0 To 9
h(i) += adj
If h(i) >= 0 Then Exit For
h(i) -= adj
Next
End If
 
Dim mean As Double = sum / sampleSize
 
Dim sd As Double
sum = 0.0
' Now calculate their standard deviation
For i As Integer = 1 To sampleSize
sum += (r(i) - mean) ^ 2.0
Next
sd = Sqr(sum/sampleSize)
 
' Draw a histogram of the data with interval 0.1
Dim numStars As Integer
' If sample size > 500 then normalize histogram to 500
Dim scale As Double = 1.0
If sampleSize > 500 Then scale = 500.0 / sampleSize
Print "Sample size "; sampleSize
Print
Print Using " Mean #.######"; mean;
Print Using " SD #.######"; sd
Print
For i As Integer = 0 To 9
Print Using " #.## : "; i/10.0;
Print Using "##### " ; h(i);
numStars = Int(h(i) * scale + 0.5)
Print String(numStars, "*")
Next
End Sub
 
basicStats 100
Print
basicStats 1000
Print
basicStats 10000
Print
basicStats 100000
Print
Print "Press any key to quit"
Sleep
Output:
Sample size  100

  Mean 0.485580  SD 0.269003

  0.00 :     7 *******
  0.10 :    10 **********
  0.20 :    12 ************
  0.30 :    17 *****************
  0.40 :     8 ********
  0.50 :    10 **********
  0.60 :    11 ***********
  0.70 :     9 *********
  0.80 :     9 *********
  0.90 :     7 *******

Sample size  1000

  Mean 0.504629  SD 0.292029

  0.00 :    99 **************************************************
  0.10 :    99 **************************************************
  0.20 :    93 ***********************************************
  0.30 :   108 ******************************************************
  0.40 :   101 ***************************************************
  0.50 :    97 *************************************************
  0.60 :    90 *********************************************
  0.70 :   110 *******************************************************
  0.80 :   102 ***************************************************
  0.90 :   101 ***************************************************

Sample size  10000

  Mean 0.500027  SD 0.290618

  0.00 :  1039 ****************************************************
  0.10 :   997 **************************************************
  0.20 :   978 *************************************************
  0.30 :   988 *************************************************
  0.40 :   998 **************************************************
  0.50 :   959 ************************************************
  0.60 :  1037 ****************************************************
  0.70 :  1004 **************************************************
  0.80 :   965 ************************************************
  0.90 :  1035 ****************************************************

Sample size  100000

  Mean 0.499503  SD 0.288730

  0.00 : 10194 ***************************************************
  0.10 :  9895 *************************************************
  0.20 :  9875 *************************************************
  0.30 :  9922 **************************************************
  0.40 : 10202 ***************************************************
  0.50 :  9981 **************************************************
  0.60 : 10034 **************************************************
  0.70 : 10012 **************************************************
  0.80 :  9957 **************************************************
  0.90 :  9928 **************************************************

Go[edit]

package main
 
import (
"fmt"
"math"
"math/rand"
"strings"
)
 
func main() {
sample(100)
sample(1000)
sample(10000)
}
 
func sample(n int) {
// generate data
d := make([]float64, n)
for i := range d {
d[i] = rand.Float64()
}
// show mean, standard deviation
var sum, ssq float64
for _, s := range d {
sum += s
ssq += s * s
}
fmt.Println(n, "numbers")
m := sum / float64(n)
fmt.Println("Mean: ", m)
fmt.Println("Stddev:", math.Sqrt(ssq/float64(n)-m*m))
// show histogram
h := make([]int, 10)
for _, s := range d {
h[int(s*10)]++
}
for _, c := range h {
fmt.Println(strings.Repeat("*", c*205/int(n)))
}
fmt.Println()
}
Output:
100 numbers
Mean:   0.5231064889267764
Stddev: 0.292668237816841
****************
****************
************************
**********************
******************
******************
****************
**************************
************************
********************

1000 numbers
Mean:   0.496026080160094
Stddev: 0.2880988956436907
*********************
********************
*****************
***********************
******************
**********************
********************
*********************
******************
*******************

10000 numbers
Mean:   0.5009091903581223
Stddev: 0.289269693719711
*******************
********************
********************
********************
*********************
********************
*******************
*******************
********************
*********************

The usual approach to the extra problem is sampling. That is, to not do it.

To show really show how computations could be done a trillion numbers however, here is an outline of a map reduce strategy. The main task indicated that numbers should be generated before doing any computations on them. Consistent with that, The function getSegment returns data based on a starting and ending index, as if it were accessing some large data store.

The following runs comfortably on a simulated data size of 10 million. To scale to a trillion, and to use real data, you would want to use a technique like Distributed_programming#Go to distribute work across multiple computers, and on each computer, use a technique like Parallel_calculations#Go to distribute work across multiple cores within each computer. You would tune parameters like the constant threshold in the code below to optimize cache performance.

package main
 
import (
"fmt"
"math"
"math/rand"
"strings"
)
 
func main() {
bigSample(1e7)
}
 
func bigSample(n int64) {
sum, ssq, h := reduce(0, n)
// compute final statistics and output as above
fmt.Println(n, "numbers")
m := sum / float64(n)
fmt.Println("Mean: ", m)
fmt.Println("Stddev:", math.Sqrt(ssq/float64(n)-m*m))
for _, c := range h {
fmt.Println(strings.Repeat("*", c*205/int(n)))
}
fmt.Println()
}
 
const threshold = 1e6
 
func reduce(start, end int64) (sum, ssq float64, h []int) {
n := end - start
if n < threshold {
d := getSegment(start, end)
return computeSegment(d)
}
// map to two sub problems
half := (start + end) / 2
sum1, ssq1, h1 := reduce(start, half)
sum2, ssq2, h2 := reduce(half, end)
// combine results
for i, c := range h2 {
h1[i] += c
}
return sum1 + sum2, ssq1 + ssq2, h1
}
 
func getSegment(start, end int64) []float64 {
d := make([]float64, end-start)
for i := range d {
d[i] = rand.Float64()
}
return d
}
 
func computeSegment(d []float64) (sum, ssq float64, h []int) {
for _, s := range d {
sum += s
ssq += s * s
}
h = make([]int, 10)
for _, s := range d {
h[int(s*10)]++
}
return
}
Output:
10000000 numbers
Mean:   0.4999673191148989
Stddev: 0.2886663876567514
********************
********************
********************
********************
********************
********************
********************
********************
********************
********************

Haskell[edit]

import Data.Foldable (foldl') --'
import System.Random (randomRs, newStdGen)
import Control.Monad (zipWithM_)
import System.Environment (getArgs)
 
intervals :: [(Double, Double)]
intervals = map conv [0 .. 9]
where
xs = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]
conv s =
let [h, l] = take 2 $ drop s xs
in (h, l)
 
count :: [Double] -> [Int]
count rands = map (\iv -> foldl'' (loop iv) 0 rands) intervals
where
loop :: (Double, Double) -> Int -> Double -> Int
loop (lo, hi) n x
| lo <= x && x < hi = n + 1
| otherwise = n
 
-- ^ fuses length and filter within (lo,hi)
data Pair a b =
Pair !a
!b
 
-- accumulate sum and length in one fold
sumLen :: [Double] -> Pair Double Double
sumLen = fion2 . foldl'' (\(Pair s l) x -> Pair (s + x) (l + 1)) (Pair 0.0 0)
where
fion2 :: Pair Double Int -> Pair Double Double
fion2 (Pair s l) = Pair s (fromIntegral l)
 
-- safe division on pairs
divl :: Pair Double Double -> Double
divl (Pair _ 0.0) = 0.0
divl (Pair s l) = s / l
 
-- sumLen and divl are separate for stddev below
mean :: [Double] -> Double
mean = divl . sumLen
 
stddev :: [Double] -> Double
stddev xs = sqrt $ foldl'' (\s x -> s + (x - m) ^ 2) 0 xs / l
where
p@(Pair s l) = sumLen xs
m = divl p
 
main = do
nr <- read . head <$> getArgs
-- or in code, e.g. let nr = 1000
rands <- take nr . randomRs (0.0, 1.0) <$> newStdGen
putStrLn $ "The mean is " ++ show (mean rands) ++ " !"
putStrLn $ "The standard deviation is " ++ show (stddev rands) ++ " !"
zipWithM_
(\iv fq -> putStrLn $ ivstr iv ++ ": " ++ fqstr fq)
intervals
(count rands)
where
fqstr i =
replicate
(if i > 50
then div i (div i 50)
else i)
'*'
ivstr (lo, hi) = show lo ++ " - " ++ show hi
 
-- To avoid Wiki formatting issue
foldl'' = foldl'
Output:
./Statistics 100
The mean is 0.5007604927009823 !
The standard deviation is 0.2933668702954616 !
0.0 - 0.1: ********
0.1 - 0.2: ************
0.2 - 0.3: ***********
0.3 - 0.4: *************
0.4 - 0.5: *****
0.5 - 0.6: ************
0.6 - 0.7: *********
0.7 - 0.8: ********
0.8 - 0.9: *********
0.9 - 1.0: *************
./Statistics 10000
The mean is 0.49399049116152155 !
The standard deviation is 0.28782134281196275 !
0.0 - 0.1: **************************************************
0.1 - 0.2: **************************************************
0.2 - 0.3: ***************************************************
0.3 - 0.4: **************************************************
0.4 - 0.5: **************************************************
0.5 - 0.6: ***************************************************
0.6 - 0.7: ***************************************************
0.7 - 0.8: ***************************************************
0.8 - 0.9: ****************************************************
0.9 - 1.0: ***************************************************

Hy[edit]

(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[edit]

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[edit]

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[edit]

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: **************************************************

Lasso[edit]

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: ++++++++++++++++++++++++

Liberty BASIC[edit]

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
 
100000 data terms used.
Mean =0.49870232
Stddev =0.28926563
######################################################################
######################################################################
######################################################################
######################################################################
#####################################################################
#####################################################################
#####################################################################
#####################################################################
######################################################################
#####################################################################

Lua[edit]

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[edit]

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[edit]

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

Mma basicstat.PNG

MATLAB / Octave[edit]

  % Initialize
N = 0; S=0; S2 = 0;
binlist = 0:.1:1;
h = zeros(1,length(binlist)); % initialize histogram
 
% read data and perform computation
while (1)
% read next sample x
if (no_data_available) break; end;
N = N + 1;
S = S + x;
S2= S2+ x*x;
ix= sum(x < binlist);
h(ix) = h(ix)+1;
end
 
% generate output
m = S/N; % mean
sd = sqrt(S2/N-mean*mean); % standard deviation
bar(binlist,h)

Nim[edit]

import math, strutils
randomize()
 
proc sd(ns): auto =
var sx, sxx = 0.0
for x in ns:
sx += x
sxx += x * x
let sd = if ns.len > 0: sqrt(float(ns.len) * sxx - sx * sx) / float(ns.len)
else: 0
(sd, sx / float(ns.len))
 
proc histogram(ns) =
var h = newSeq[int](10)
for n in ns:
let pos = int(n * 10)
inc h[pos]
 
const maxWidth = 50
let mx = max(h)
echo ""
for n, i in h:
echo n/10,": ",repeatChar(int(i / mx * maxWidth), '+')
echo ""
 
for i in [10, 100, 1_000, 10_000, 100_000]:
var n = newSeq[float](i)
for x in 0..n.high: n[x] = random(1.0)
echo "\n##\n## ",i," numbers\n##"
let (sd, mean) = sd(n)
echo "sd: ",sd,", mean: ",mean
histogram(n)
Output:
##
## 10 numbers
##
sd: 0.2738118959385979, mean: 0.4717111448227304

0.0: +++++++++++++++++++++++++
0.1: +++++++++++++++++++++++++
0.2: 
0.3: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.5: 
0.6: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++
0.8: 
0.9: +++++++++++++++++++++++++

[...]

##
## 100000 numbers
##
sd: 0.2884329643843962, mean: 0.4997598571602153

0.0: ++++++++++++++++++++++++++++++++++++++++++++++++
0.1: +++++++++++++++++++++++++++++++++++++++++++++++++
0.2: ++++++++++++++++++++++++++++++++++++++++++++++++
0.3: +++++++++++++++++++++++++++++++++++++++++++++++++
0.4: ++++++++++++++++++++++++++++++++++++++++++++++++
0.5: ++++++++++++++++++++++++++++++++++++++++++++++++
0.6: ++++++++++++++++++++++++++++++++++++++++++++++++++
0.7: +++++++++++++++++++++++++++++++++++++++++++++++++
0.8: +++++++++++++++++++++++++++++++++++++++++++++++++
0.9: ++++++++++++++++++++++++++++++++++++++++++++++++

Oforth[edit]

: 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[edit]

Works with: PARI/GP version 2.4.3 and above
mean(v)={
sum(i=1,#v,v[i])/#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[edit]

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 : *******************************

Perl 6[edit]

Works with: rakudo version 2017.01
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	==================================================

PicoLisp[edit]

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.

(scl 6)
 
(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) ) ) )

Test:

(statistics 100
(rand 0 (dec 1.0)) )
(prinl)
 
(statistics 10000
(rand 0 (dec 1.0)) )
(prinl)
 
(statistics 1000000
(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[edit]

 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 

PureBasic[edit]

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
##################################################################
################################################################
##################################################################
####################################################################
################################################################
######################################################################
####################################################################
###################################################################
####################################################################
####################################################################

Python[edit]

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: +++++++++++++++++++++++++++++++++++++++++++++++++

Racket[edit]

 
#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: *******************

REXX[edit]

/*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(0, 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('─', format(barPC*1, , 0)) /*display 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: parse arg N; $=0; do m=1 for N; $=$+@.m; end; return $/n
stdDev: parse arg N; $=0; do s=1 for N; $=$+(@.s-avg)**2; end; return sqrt($/n)
/*──────────────────────────────────────────────────────────────────────────────────────*/
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/1

output   when using the default input of:   100

0  ──►0.1  12.00 ────────────
0.1──►0.2   9.00 ─────────
0.2──►0.3   9.00 ─────────
0.3──►0.4  11.00 ───────────
0.4──►0.5   6.00 ──────
0.5──►0.6   9.00 ─────────
0.6──►0.7   8.00 ────────
0.7──►0.8  15.00 ───────────────
0.8──►0.9   8.00 ────────
0.9──►1    13.00 ─────────────

sample size =  100

       mean =  0.5116398000
     stdDev =  0.3045475491

output   when using the input of:   1000

0  ──►0.1   8.60 ─────────
0.1──►0.2  10.70 ───────────
0.2──►0.3  10.00 ──────────
0.3──►0.4   9.40 ─────────
0.4──►0.5  10.30 ──────────
0.5──►0.6  11.20 ───────────
0.6──►0.7  10.50 ───────────
0.7──►0.8   8.20 ────────
0.8──►0.9  10.60 ───────────
0.9──►1    10.50 ───────────

sample size =  1000

       mean =  0.5050967300
     stdDev =  0.2862526217

output   when using the input of:   10000

0  ──►0.1  10.19 ──────────
0.1──►0.2   9.95 ──────────
0.2──►0.3  10.15 ──────────
0.3──►0.4   9.51 ──────────
0.4──►0.5   9.62 ──────────
0.5──►0.6  10.00 ──────────
0.6──►0.7  10.73 ───────────
0.7──►0.8  10.25 ──────────
0.8──►0.9   9.48 ─────────
0.9──►1    10.12 ──────────

sample size =  10000

       mean =  0.5003715510
     stdDev =  0.2889881184

output   when using the input of:   100000

0  ──►0.1  10.02 ──────────
0.1──►0.2  10.00 ──────────
0.2──►0.3   9.92 ──────────
0.3──►0.4  10.03 ──────────
0.4──►0.5   9.91 ──────────
0.5──►0.6  10.11 ──────────
0.6──►0.7   9.93 ──────────
0.7──►0.8  10.14 ──────────
0.8──►0.9  10.04 ──────────
0.9──►1     9.90 ──────────

sample size =  100000

       mean =  0.5000565186
     stdDev =  0.2885638076

output   when using the input of:   1000000

0  ──►0.1   9.98 ──────────
0.1──►0.2  10.01 ──────────
0.2──►0.3   9.96 ──────────
0.3──►0.4   9.99 ──────────
0.4──►0.5  10.05 ──────────
0.5──►0.6  10.01 ──────────
0.6──►0.7   9.98 ──────────
0.7──►0.8  10.03 ──────────
0.8──►0.9   9.99 ──────────
0.9──►1     9.99 ──────────

sample size =  1000000

       mean =  0.5001575274
     stdDev =  0.2885531446

Ruby[edit]

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:=================================================================


Run BASIC[edit]

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

Rust[edit]

#![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[edit]

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[edit]

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 = Math.sqrt(sum2/n - mean**2);
 
say "size: #{n}";
say "mean: #{mean}";
say "stddev: #{stddev}";
 
var max = hist.max;
hist.range.each {|i|
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:   0.4585051431752446588
stddev: 0.2870559459562831101619581273667538623484
0.0:=================================================================
0.1:==================================================
0.2:======================================================================
0.3:=============================================
0.4:=======================================================
0.5:==============================
0.6:==================================================
0.7:==================================================
0.8:==================================================
0.9:===================================

size: 1000
mean:   0.51292239343467439552
stddev: 0.2832968595790956540009121237087699143503
0.0:===================================================
0.1:========================================================
0.2:========================================================
0.3:========================================================
0.4:======================================================================
0.5:==================================================================
0.6:===============================================================
0.7:=========================================================
0.8:========================================================
0.9:====================================================================

size: 10000
mean:   0.49883638025449614521145
stddev: 0.2898083000452161646017460189689302069547
0.0:====================================================================
0.1:============================================================
0.2:======================================================================
0.3:==============================================================
0.4:===============================================================
0.5:=================================================================
0.6:===============================================================
0.7:=================================================================
0.8:==================================================================
0.9:===============================================================

Tcl[edit]

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.)

zkl[edit]

fcn mean(ns)  { ns.sum(0.0)/ns.len() }
fcn stdDev(ns){
m:=mean(ns); (ns.reduce('wrap(p,n){ x:=(n-m); p+x*x },0.0)/ns.len()).sqrt()
}
reg ns;
foreach n in (T(100,1000,10000)){
ns=(0).pump(n,List,(0.0).random.fp(1.0));
println("N:%,6d mean:%.5f std dev:%.5f".fmt(n,mean(ns),stdDev(ns)));
}
foreach r in ([0.0 .. 0.9, 0.1]){ // using the last data set (10000 randoms)
n:=ns.filter('wrap(x){ r<=x<(r+0.1) }).len();
println("%.2f..%.2f:%4d%s".fmt(r,r+0.1,n,"*"*(n/20)));
}

(0.0).random(1.0) generates a [uniform] random number between 0 (inclusive) and 1 (exclusive).

Output:
N:   100  mean:0.48521 std dev:0.27073
N: 1,000  mean:0.49362 std dev:0.28921
N:10,000  mean:0.49899 std dev:0.28813
0.00..0.10: 986*************************************************
0.10..0.20:1043****************************************************
0.20..0.30: 992*************************************************
0.30..0.40: 974************************************************
0.40..0.50:1001**************************************************
0.50..0.60: 998*************************************************
0.60..0.70: 995*************************************************
0.70..0.80:1043****************************************************
0.80..0.90:1005**************************************************
0.90..1.00: 963************************************************

For the extra credit, pretend we have a device that spews random numbers in the range [0..1) forever. We connect this device to a measuring device that calculates mean and std deviation, printing results on a regular basis.

var pipe=Thread.Pipe(); // used to connect the two threads
fcn{ while(1){ pipe.write((0.0).random(1.0)) } }.launch(); // generator
fcn{ // consumer/calculator
N:=0; M:=SD:=sum:=ssum:=0.0;
while(1){
x:=pipe.read(); N+=1; sum+=x; ssum+=x*x;
M=sum/N; SD=(ssum/N - M*M).sqrt();
if(0==N%100000)
println("N:%,10d mean:%.5f std dev:%.5f".fmt(N,M,SD));
}
}.launch();
 
Atomic.sleep(60*60); // wait because exiting the VM kills the threads
Output:
...
N:45,800,000  mean:0.49997 std dev:0.28869
N:45,900,000  mean:0.49997 std dev:0.28869
N:46,000,000  mean:0.49997 std dev:0.28869
N:46,100,000  mean:0.49998 std dev:0.28869
N:46,200,000  mean:0.49997 std dev:0.28870
N:46,300,000  mean:0.49997 std dev:0.28870
N:46,400,000  mean:0.49997 std dev:0.28870
...