Standard deviation
From Rosetta Code
You are encouraged to solve this task according to the task description, using any language you may know.
Write a stateful function, class, generator or coroutine that takes a series of floating point numbers, one at a time, and returns the running standard deviation of the series. The task implementation should use the most natural programming style of those listed for the function in the implementation language; the task must state which is being used. Do not apply Bessel's correction; the returned standard deviation should always be computed as if the sample seen so far is the entire population.
Use this to compute the standard deviation of this demonstration set, {2,4,4,4,5,5,7,9}, which is 2.
See also: Moving Average
[edit] Ada
with Ada.Numerics.Elementary_Functions; use Ada.Numerics.Elementary_Functions;
with Ada.Text_IO; use Ada.Text_IO;
procedure Test_Deviation is
type Sample is record
N : Natural := 0;
Mean : Float := 0.0;
Squares : Float := 0.0;
end record;
procedure Add (Data : in out Sample; Point : Float) is
begin
Data.N := Data.N + 1;
Data.Mean := Data.Mean + Point;
Data.Squares := Data.Squares + Point ** 2;
end Add;
function Deviation (Data : Sample) return Float is
begin
return Sqrt (Data.Squares / Float (Data.N) - (Data.Mean / Float (Data.N)) ** 2);
end Deviation;
Data : Sample;
Test : array (1..8) of Float := (2.0, 4.0, 4.0, 4.0, 5.0, 5.0, 7.0, 9.0);
begin
for Item in Test'Range loop
Add (Data, Test (Item));
end loop;
Put_Line ("Deviation" & Float'Image (Deviation (Data)));
end Test_Deviation;
Sample output:
Deviation 2.00000E+00
[edit] ALGOL 68
Note: the use of a UNION to mimic C's enumerated types is "experimental" and probably not typical of "production code". However it is a example of ALGOL 68s conformity CASE clause useful for classroom dissection.
MODE VALUE = STRUCT(CHAR value),Output:
STDDEV = STRUCT(CHAR stddev),
MEAN = STRUCT(CHAR mean),
VAR = STRUCT(CHAR var),
COUNT = STRUCT(CHAR count),
RESET = STRUCT(CHAR reset);
MODE ACTION = UNION ( VALUE, STDDEV, MEAN, VAR, COUNT, RESET );
LONG REAL sum := 0;
LONG REAL sum2 := 0;
INT num := 0;
PROC stat object = (LONG REAL v, ACTION action)LONG REAL:
(
LONG REAL m;
CASE action IN
(VALUE):(
num +:= 1;
sum +:= v;
sum2 +:= v*v;
stat object(0, LOC STDDEV)
),
(STDDEV):
long sqrt(stat object(0, LOC VAR)),
(MEAN):
IF num>0 THEN sum/LONG REAL(num) ELSE 0 FI,
(VAR):(
m := stat object(0, LOC MEAN);
IF num>0 THEN sum2/LONG REAL(num)-m*m ELSE 0 FI
),
(COUNT):
num,
(RESET):
sum := sum2 := num := 0
ESAC
);
[]LONG REAL v = ( 2,4,4,4,5,5,7,9 );
main:
(
LONG REAL sd;
FOR i FROM LWB v TO UPB v DO
sd := stat object(v[i], LOC VALUE)
OD;
printf(($"standard dev := "g(0,6)l$, sd))
)
standard dev := 2.000000
A code sample in an object oriented style:
MODE STAT = STRUCT(Output:
LONG REAL sum,
LONG REAL sum2,
INT num
);
OP INIT = (REF STAT new)REF STAT:
(init OF class stat)(new);
MODE CLASSSTAT = STRUCT(
PROC (REF STAT, LONG REAL #value#)VOID plusab,
PROC (REF STAT)LONG REAL stddev, mean, variance, count,
PROC (REF STAT)REF STAT init
);
CLASSSTAT class stat;
plusab OF class stat := (REF STAT self, LONG REAL value)VOID:(
num OF self +:= 1;
sum OF self +:= value;
sum2 OF self +:= value*value
);
OP +:= = (REF STAT lhs, LONG REAL rhs)VOID: # some syntatic sugar #
(plusab OF class stat)(lhs, rhs);
stddev OF class stat := (REF STAT self)LONG REAL:
long sqrt((variance OF class stat)(self));
OP STDDEV = ([]LONG REAL value)LONG REAL: ( # more syntatic sugar #
REF STAT stat = INIT LOC STAT;
FOR i FROM LWB value TO UPB value DO
stat +:= value[i]
OD;
(stddev OF class stat)(stat)
);
mean OF class stat := (REF STAT self)LONG REAL:
sum OF self/LONG REAL(num OF self);
variance OF class stat := (REF STAT self)LONG REAL:(
LONG REAL m = (mean OF class stat)(self);
sum2 OF self/LONG REAL(num OF self)-m*m
);
count OF class stat := (REF STAT self)LONG REAL:
num OF self;
init OF class stat := (REF STAT self)REF STAT:(
sum OF self := sum2 OF self := num OF self := 0;
self
);
[]LONG REAL value = ( 2,4,4,4,5,5,7,9 );
main:
(
printf(($"standard deviation operator = "g(0,6)l$, STDDEV value));
REF STAT stat = INIT LOC STAT;
FOR i FROM LWB value TO UPB value DO
stat +:= value[i]
OD;
printf(($"standard deviation = "g(0,6)l$, (stddev OF class stat)(stat)));
printf(($"mean = "g(0,6)l$, (mean OF class stat)(stat)));
printf(($"variance = "g(0,6)l$, (variance OF class stat)(stat)));
printf(($"count = "g(0,6)l$, (count OF class stat)(stat)))
)
standard deviation operator = 2.000000 standard deviation = 2.000000 mean = 5.000000 variance = 4.000000 count = 8.000000
A simple - but "unpackaged" - code example, useful if the standard deviation is required on only one set of concurrent data:
LONG REAL sum, sum2;Output:
INT n;
PROC sd = (LONG REAL x)LONG REAL:(
sum +:= x;
sum2 +:= x*x;
n +:= 1;
IF n = 0 THEN 0 ELSE long sqrt(sum2/n - sum*sum/n/n) FI
);
sum := sum2 := n := 0;
[]LONG REAL values = (2,4,4,4,5,5,7,9);
FOR i TO UPB values DO
LONG REAL value = values[i];
printf(($2(xg(0,6))l$, value, sd(value)))
OD
2.000000 .000000 4.000000 1.000000 4.000000 .942809 4.000000 .866025 5.000000 .979796 5.000000 1.000000 7.000000 1.399708 9.000000 2.000000
[edit] AutoHotkey
ahk forum: discussion
std(2),std(4),std(4),std(4),std(5),std(5),std(7)
MsgBox % std(9) ; 2
std(x="") {
Static sum:=0, sqr:=0, n:=0
If (x="") ; blank parameter: reset
sum := 0, sqr := 0, n := 0
Else
sum += x, sqr += x*x, n++ ; update state
Return sqrt((sqr-sum*sum/n)/n)
}
[edit] Axiom
We implement a domain with dependent type T with the operation + and identity 0:)abbrev package TESTD TestDomainThis can be called using:
TestDomain(T : Join(Field,RadicalCategory)): Exports == Implementation where
R ==> Record(n : Integer, sum : T, ssq : T)
Exports == AbelianMonoid with
_+ : (%,T) -> %
_+ : (T,%) -> %
sd : % -> T
Implementation == R add
Rep := R -- similar representation and implementation
obj : %
0 == [0,0,0]
obj + (obj2:%) == [obj.n + obj2.n, obj.sum + obj2.sum, obj.ssq + obj2.ssq]
obj + (x:T) == obj + [1, x, x*x]
(x:T) + obj == obj + x
sd obj ==
mean : T := obj.sum / (obj.n::T)
sqrt(obj.ssq / (obj.n::T) - mean*mean)
T ==> Expression Integer
D ==> TestDomain(T)
items := [2,4,4,4,5,5,7,9+x] :: List T;
map(sd, scan(+, items, 0$D))
+---------------+
+-+ +-+ +-+ +-+ | 2
2\|2 \|3 2\|6 4\|6 \|7x + 64x + 256
(1) [0,1,-----,----,-----,1,-----,------------------]
3 2 5 7 8
Type: List(Expression(Integer))
eval subst(last %,x=0)
(2) 2
Type: Expression(Integer)
[edit] BBC BASIC
Uses the MOD(array()) and SUM(array()) functions.
MAXITEMS = 100
FOR i% = 1 TO 8
READ n
PRINT "Value = "; n ", running SD = " FNrunningsd(n)
NEXT
END
DATA 2,4,4,4,5,5,7,9
DEF FNrunningsd(n)
PRIVATE list(), i%
DIM list(MAXITEMS)
i% += 1
list(i%) = n
= SQR(MOD(list())^2/i% - (SUM(list())/i%)^2)
Output:
Value = 2, running SD = 0 Value = 4, running SD = 1 Value = 4, running SD = 0.942809043 Value = 4, running SD = 0.866025404 Value = 5, running SD = 0.979795901 Value = 5, running SD = 1 Value = 7, running SD = 1.39970842 Value = 9, running SD = 2
[edit] C
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
enum Action { STDDEV, MEAN, VAR, COUNT };
typedef struct stat_obj_struct {
double sum, sum2;
size_t num;
Action action;
} sStatObject, *StatObject;
StatObject NewStatObject( Action action )
{
so = malloc(sizeof(sStatObject));
so->sum = 0.0;
so->sum2 = 0.0;
so->num = 0;
so->action = action;
return so;
}
#define FREE_STAT_OBJECT(so) \
free(so); so = NULL
double stat_obj_value(StatObject so, Action action)
{
double num, mean, var, stddev;
if (so->num == 0.0) return 0.0;
num = so->num;
if (action==COUNT) return num;
mean = so->sum/num;
if (action==MEAN) return mean;
var = so->sum2/num - mean*mean;
if (action==VAR) return var;
stddev = sqrt(var);
if (action==STDDEV) return stddev;
return 0;
}
double stat_object_add(StatObject so, double v)
{
so->num++;
so->sum += v;
so->sum2 += v*v;
return stat_obj_value(so->action);
}
double v[] = { 2,4,4,4,5,5,7,9 };
int main()
{
int i;
StatObject so = NewStatObject( STDDEV );
for(i=0; i < sizeof(v)/sizeof(double) ; i++)
printf("val: %lf std dev: %lf\n", v[i], stat_object_add(so, v[i]));
FREE_STAT_OBJECT(so);
return 0;
}
[edit] C++
#include <algorithm>
#include <iostream>
#include <iterator>
#include <cmath>
#include <vector>
#include <iterator>
#include <numeric>
template <typename Iterator>
double standard_dev( Iterator begin , Iterator end ) {
double mean = std::accumulate( begin , end , 0 ) / std::distance( begin , end ) ;
std::vector<double> squares ;
for( Iterator vdi = begin ; vdi != end ; vdi++ )
squares.push_back( std::pow( *vdi - mean , 2 ) ) ;
return std::sqrt( std::accumulate( squares.begin( ) , squares.end( ) , 0 ) / squares.size( ) ) ;
}
int main( ) {
double demoset[] = { 2 , 4 , 4 , 4 , 5 , 5 , 7 , 9 } ;
int demosize = sizeof demoset / sizeof *demoset ;
std::cout << "The standard deviation of\n" ;
std::copy( demoset , demoset + demosize , std::ostream_iterator<double>( std::cout, " " ) ) ;
std::cout << "\nis " << standard_dev( demoset , demoset + demosize ) << " !\n" ;
return 0 ;
}
[edit] C#
using System;
using System.Collections.Generic;
using System.Linq;
namespace standardDeviation
{
class Program
{
static void Main(string[] args)
{
List<double> nums = new List<double> { 2, 4, 4, 4, 5, 5, 7, 9 };
for (int i = 1; i <= nums.Count; i++)
Console.WriteLine(sdev(nums.GetRange(0, i)));
}
static double sdev(List<double> nums)
{
List<double> store = new List<double>();
foreach (double n in nums)
store.Add((n - nums.Average()) * (n - nums.Average()));
return Math.Sqrt(store.Sum() / store.Count);
}
}
}
0 1 0,942809041582063 0,866025403784439 0,979795897113271 1 1,39970842444753 2
[edit] Clojure
(defn std-dev [samples]
(let [n (count samples)
mean (/ (reduce + samples) n)
intermediate (map #(Math/pow (- %1 mean) 2) samples)]
(Math/sqrt
(/ (reduce + intermediate) n))))
(println (std-dev [2 4 4 4 5 5 7 9])) ;;2.0
[edit] Common Lisp
(defun std-dev (samples)
(let* ((n (length samples))
(mean (/ (reduce #'+ samples) n))
(tmp (mapcar (lambda (x) (sqr (- x mean))) samples)))
(sqrt (/ (reduce #'+ tmp) n))))
(format t "~a" (std-dev '(2 4 4 4 5 5 7 9)))
Based on some googled web site; written ages ago.
(defun arithmetic-average (samples)
(/ (reduce #'+ samples)
(length samples)))
(defun standard-deviation (samples)
(let ((mean (arithmetic-average samples)))
(sqrt (* (/ 1.0d0 (length samples))
(reduce #'+ samples
:key (lambda (x)
(expt (- x mean) 2)))))))
(defun make-deviator ()
(let ((numbers '()))
(lambda (x)
(push x numbers)
(standard-deviation numbers))))
CL-USER> (loop with deviator = (make-deviator)Since we don't care about the sample values once std dev is computed, we only need to keep track of their sum and square sums, hence:
for i in '(2 4 4 4 5 5 7 9)
collect (list i (funcall deviator i))) ==>
((2 0.0d0)
(4 1.0d0)
(4 0.9428090415820634d0)
(4 0.8660254037844386d0)
(5 0.9797958971132713d0)
(5 1.0d0)
(7 1.3997084244475304d0)
(9 2.0d0))
(defun running-stddev ()
(let ((sum 0) (sq 0) (n 0))
(lambda (x)
(incf sum x) (incf sq (* x x)) (incf n)
(/ (sqrt (- (* n sq) (* sum sum))) n))))
(loop with f = (running-stddev) for i in '(2 4 4 4 5 5 7 9) do
(format t "~a ~a~%" i (funcall f i)))
[edit] D
import std.stdio, std.math;
struct StdDev {
real sum = 0.0, sqSum = 0.0;
long nvalues;
void addNumber(in real input) pure nothrow {
nvalues++;
sum += input;
sqSum += input ^^ 2;
}
real getStdDev() const pure nothrow {
if (nvalues == 0)
return 0.0;
immutable real mean = sum / nvalues;
return sqrt(sqSum / nvalues - mean ^^ 2);
}
}
void main() {
StdDev stdev;
foreach (el; [2.0, 4, 4, 4, 5, 5, 7, 9]) {
stdev.addNumber(el);
writefln("%e", stdev.getStdDev());
}
}
Output:
0.000000e+00 1.000000e+00 9.428090e-01 8.660254e-01 9.797959e-01 1.000000e+00 1.399708e+00 2.000000e+00
[edit] Delphi
Delphi has 2 functions in Math unit for standard deviation: StdDev (with Bessel correction) and PopnStdDev (without Bessel correction). The task assumes the second function:
program StdDevTest;
{$APPTYPE CONSOLE}
uses
Math;
begin
Writeln(PopnStdDev([2,4,4,4,5,5,7,9]));
Readln;
end.
[edit] E
This implementation produces two (function) objects sharing state. It is idiomatic in E to separate input from output (read from write) rather than combining them into one object.
The algorithm is and the results were checked against #Python.def makeRunningStdDev() {
var sum := 0.0
var sumSquares := 0.0
var count := 0.0
def insert(v) {
sum += v
sumSquares += v ** 2
count += 1
}
/** Returns the standard deviation of the inputs so far, or null if there
have been no inputs. */
def stddev() {
if (count > 0) {
def meanSquares := sumSquares/count
def mean := sum/count
def variance := meanSquares - mean**2
return variance.sqrt()
}
}
return [insert, stddev]
}
? def [insert, stddev] := makeRunningStdDev()
# value: <insert>, <stddev>
? [stddev()]
# value: [null]
? for value in [2,4,4,4,5,5,7,9] {
> insert(value)
> println(stddev())
> }
0.0
1.0
0.9428090415820626
0.8660254037844386
0.9797958971132716
1.0
1.3997084244475297
2.0
==Emacs Lisp==e
This implementation uses a temporary buffer (the central data structure of emacs) to have simple local variables.
(defun running-std (x)
; ensure that we have a float to avoid potential integer math errors.
(setq x (float x))
; define variables to use
(defvar running-sum 0 "the running sum of all known values")
(defvar running-len 0 "the running number of all known values")
(defvar running-squared-sum 0 "the running squared sum of all known values")
; and make them local to this buffer
(make-local-variable 'running-sum)
(make-local-variable 'running-len)
(make-local-variable 'running-squared-sum)
; now process the new value
(setq running-sum (+ running-sum x))
(setq running-len (1+ running-len))
(setq running-squared-sum (+ running-squared-sum (* x x)))
; and calculate the new standard deviation
(sqrt (- (/ running-squared-sum
running-len) (/ (* running-sum running-sum)
(* running-len running-len )))))
(with-temp-buffer
(loop for i in '(2 4 4 4 5 5 7 9) do
(insert (number-to-string (running-std i)))
(newline))
(message (buffer-substring (point-min) (1- (point-max)))))
"0.0
1.0
0.9428090415820636
0.8660254037844386
0.9797958971132716
1.0
1.399708424447531
2.0"
[edit] Emacs Lisp
This implementation uses a temporary buffer (the central data structure of emacs) to have simple local variables.
(defun running-std (x)
; ensure that we have a float to avoid potential integer math errors.
(setq x (float x))
; define variables to use
(defvar running-sum 0 "the running sum of all known values")
(defvar running-len 0 "the running number of all known values")
(defvar running-squared-sum 0 "the running squared sum of all known values")
; and make them local to this buffer
(make-local-variable 'running-sum)
(make-local-variable 'running-len)
(make-local-variable 'running-squared-sum)
; now process the new value
(setq running-sum (+ running-sum x))
(setq running-len (1+ running-len))
(setq running-squared-sum (+ running-squared-sum (* x x)))
; and calculate the new standard deviation
(sqrt (- (/ running-squared-sum
running-len) (/ (* running-sum running-sum)
(* running-len running-len )))))
(with-temp-buffer
(loop for i in '(2 4 4 4 5 5 7 9) do
(insert (number-to-string (running-std i)))
(newline))
(message (buffer-substring (point-min) (1- (point-max)))))
"0.0
1.0
0.9428090415820636
0.8660254037844386
0.9797958971132716
1.0
1.399708424447531
2.0"
[edit] Factor
USING: accessors io kernel math math.functions math.parser
sequences ;
IN: standard-deviator
TUPLE: standard-deviator sum sum^2 n ;
: <standard-deviator> ( -- standard-deviator )
0.0 0.0 0 standard-deviator boa ;
: current-std ( standard-deviator -- std )
[ [ sum^2>> ] [ n>> ] bi / ]
[ [ sum>> ] [ n>> ] bi / sq ] bi - sqrt ;
: add-value ( value standard-deviator -- )
[ nip [ 1 + ] change-n drop ]
[ [ + ] change-sum drop ]
[ [ [ sq ] dip + ] change-sum^2 drop ] 2tri ;
: main ( -- )
{ 2 4 4 4 5 5 7 9 }
<standard-deviator> [ [ add-value ] curry each ] keep
current-std number>string print ;
[edit] Forth
: f+! ( x addr -- ) dup f@ f+ f! ;
: st-count ( stats -- n ) f@ ;
: st-sum ( stats -- sum ) float+ f@ ;
: st-sumsq ( stats -- sum*sum ) 2 floats + f@ ;
: st-add ( fnum stats -- )
1e dup f+! float+
fdup dup f+! float+
fdup f* f+! ;
: st-mean ( stats -- mean )
dup st-sum st-count f/ ;
: st-variance ( stats -- var )
dup st-sumsq
dup st-mean fdup f* dup st-count f* f-
st-count f/ ;
: st-stddev ( stats -- stddev )
st-variance fsqrt ;
This variation is more numerically stable when there are large numbers of samples or large sample ranges.
: st-count ( stats -- n ) f@ ;
: st-mean ( stats -- mean ) float+ f@ ;
: st-nvar ( stats -- n*var ) 2 floats + f@ ;
: st-variance ( stats -- var ) dup st-nvar st-count f/ ;
: st-stddev ( stats -- stddev ) st-variance fsqrt ;
: st-add ( x stats -- )
1e dup f+! \ update count
fdup dup st-mean f- fswap
( delta x )
fover dup st-count f/
( delta x delta/n )
float+ dup f+! \ update mean
( delta x )
dup f@ f- f* float+ f+! ; \ update nvar
create stats 0e f, 0e f, 0e f,
2e stats st-add
4e stats st-add
4e stats st-add
4e stats st-add
5e stats st-add
5e stats st-add
7e stats st-add
9e stats st-add
stats st-stddev f. \ 2.
[edit] Fortran
This one imitates C and suffers the same problems: the function is not thread-safe and must be used to compute the stddev for one set per time.
program Test_Stddev
implicit none
real, dimension(8) :: v = (/ 2,4,4,4,5,5,7,9 /)
integer :: i
real :: sd
do i = 1, size(v)
sd = stat_object(v(i))
end do
print *, "std dev = ", sd
contains
recursive function stat_object(a, cmd) result(stddev)
real :: stddev
real, intent(in) :: a
character(len=*), intent(in), optional :: cmd
real, save :: summa = 0.0, summa2 = 0.0
integer, save :: num = 0
real :: m
if ( .not. present(cmd) ) then
num = num + 1
summa = summa + a
summa2 = summa2 + a*a
stddev = stat_object(0.0, "stddev")
else
select case(cmd)
case("stddev")
stddev = sqrt(stat_object(0.0, "variance"))
case("variance")
m = stat_object(0.0, "mean")
if ( num > 0 ) then
stddev = summa2/real(num) - m*m
else
stddev = 0.0
end if
case("count")
stddev = real(num)
case("mean")
if ( num > 0 ) then
stddev = summa/real(num)
else
stddev = 0.0
end if
case("reset")
summa = 0.0
summa2 = 0.0
num = 0
case default
stddev = 0.0
end select
end if
end function stat_object
end program Test_Stddev
[edit] Using built-in array awareness
This uses Fortran's built-in array features (which aren't available in C)
program stats
implicit none
integer, parameter :: N = 8
integer :: data(N)
real(8) :: mean
real(8) :: std_dev1, std_dev2
! Set the data
data = [2,4,4,4,5,5,7,9] ! Strictly this is a Fortran 2003 construct
! Use intrinsic function 'sum' to calculate the mean
mean = sum(data)/N
! Method1:
! Calculate the standard deviation directly from the definition
std_dev1 = sqrt(sum((data - mean)**2)/N)
! Method 2:
! Use the alternative version that is less susceptible to rounding error
std_dev2 = sqrt(sum(data**2)/N - mean**2)
write(*,'(a,8i2)') 'Data = ',data
write(*,'(a,f3.1)') 'Mean = ',mean
write(*,'(a,f3.1)') 'Standard deviation (method 1) = ',std_dev1
write(*,'(a,f3.1)') 'Standard deviation (method 2) = ',std_dev2
end program stats
[edit] Go
Algorithm to reduce rounding errors from WP article.
State maintained with a closure.
package main
import (
"fmt"
"math"
)
func newRsdv() func(float64) float64 {
var n, a, q float64
return func(x float64) float64 {
n++
a1 := a+(x-a)/n
q, a = q+(x-a)*(x-a1), a1
return math.Sqrt(q/n)
}
}
func main() {
r := newRsdv()
for _, x := range []float64{2,4,4,4,5,5,7,9} {
fmt.Println(r(x))
}
}
Output:
0 1 0.9428090415820634 0.8660254037844386 0.9797958971132713 1 1.3997084244475304 2
[edit] Groovy
Solution:
def sum = 0
def sumSq = 0
def count = 0
[2,4,4,4,5,5,7,9].each {
sum += it
sumSq += it*it
count++
println "running std.dev.: ${(sumSq/count - (sum/count)**2)**0.5}"
}
Output:
running std.dev.: 0 running std.dev.: 1 running std.dev.: 0.9428090416999145 running std.dev.: 0.8660254037844386 running std.dev.: 0.9797958971132712 running std.dev.: 1 running std.dev.: 1.3997084243469262 running std.dev.: 2
[edit] Haskell
We store the state in the ST monad using an STRef.
import Data.List (genericLength)
import Data.STRef
import Control.Monad.ST
sd :: RealFloat a => [a] -> a
sd l = sqrt $ sum (map ((^2) . subtract mean) l) / n
where n = genericLength l
mean = sum l / n
sdAccum :: RealFloat a => ST s (a -> ST s a)
sdAccum = do
accum <- newSTRef []
return $ \x -> do
modifySTRef accum (x:)
list <- readSTRef accum
return $ sd list
main = mapM_ print results
where results = runST $ do
runningSD <- sdAccum
mapM runningSD [2, 4, 4, 4, 5, 5, 7, 9]
[edit] Haxe
using Lambda;
class Main {
static function main():Void {
var nums = [2, 4, 4, 4, 5, 5, 7, 9];
for (i in 1...nums.length+1)
Sys.println(sdev(nums.slice(0, i)));
}
static function average<T:Float>(nums:Array<T>):Float {
return nums.fold(function(n, t) return n + t, 0) / nums.length;
}
static function sdev<T:Float>(nums:Array<T>):Float {
var store = [];
var avg = average(nums);
for (n in nums) {
store.push((n - avg) * (n - avg));
}
return Math.sqrt(average(store));
}
}
0 1 0.942809041582063 0.866025403784439 0.979795897113271 1 1.39970842444753 2
[edit] HicEst
REAL :: n=8, set(n), sum=0, sum2=0
set = (2,4,4,4,5,5,7,9)
DO k = 1, n
WRITE() 'Adding ' // set(k) // 'stdev = ' // stdev(set(k))
ENDDO
END ! end of "main"
FUNCTION stdev(x)
USE : sum, sum2, k
sum = sum + x
sum2 = sum2 + x*x
stdev = ( sum2/k - (sum/k)^2) ^ 0.5
END
Adding 2 stdev = 0 Adding 4 stdev = 1 Adding 4 stdev = 0.9428090416 Adding 4 stdev = 0.8660254038 Adding 5 stdev = 0.9797958971 Adding 5 stdev = 1 Adding 7 stdev = 1.399708424 Adding 9 stdev = 2
[edit] Icon and Unicon
rocedure main()Sample output:
stddev() # reset state / empty
every s := stddev(![2,4,4,4,5,5,7,9]) do
write("stddev (so far) := ",s)
end
procedure stddev(x) /: running standard deviation
static X,sumX,sum2X
if /x then { # reset state
X := []
sumX := sum2X := 0.
}
else { # accumulate
put(X,x)
sumX +:= x
sum2X +:= x^2
return sqrt( (sum2X / *X) - (sumX / *X)^2 )
}
end
stddev (so far) := 0.0 stddev (so far) := 1.0 stddev (so far) := 0.9428090415820626 stddev (so far) := 0.8660254037844386 stddev (so far) := 0.9797958971132716 stddev (so far) := 1.0 stddev (so far) := 1.39970842444753 stddev (so far) := 2.0
[edit] J
J is block-oriented; it expresses algorithms with the semantics of all the data being available at once. It does not have native lexical closure or coroutine semantics. It is possible to implement these semantics in J; see Moving Average for an example. We will not reprise that here.
mean=: +/ % #
dev=: - mean
stddevP=: [: %:@mean *:@dev NB. A) 3 equivalent defs for stddevP
stddevP=: [: mean&.:*: dev NB. B) uses Under (&.:) to apply inverse of *: after mean
stddevP=: %:@(mean@:*: - *:@mean) NB. C) sqrt of ((mean of squares) - (square of mean))
stddevP\ 2 4 4 4 5 5 7 9
0 1 0.942809 0.866025 0.979796 1 1.39971 2
Alternatives:
Using verbose names for J primitives.
of =: @:
sqrt =: %:
sum =: +/
squares=: *:
data =: ]
mean =: sum % #
stddevP=: sqrt of mean of squares of (data-mean)
stddevP\ 2 4 4 4 5 5 7 9
0 1 0.942809 0.866025 0.979796 1 1.39971 2
Or we could take a cue from the R implementation and reverse the Bessel correction to stddev:
require'stats'
(%:@:(%~<:)@:# * stddev)\ 2 4 4 4 5 5 7 9
0 1 0.942809 0.866025 0.979796 1 1.39971 2
[edit] Java
import java.util.LinkedList;
public class StdDev {
LinkedList<Double> nums;
public StdDev() {
nums = new LinkedList<Double>();
}
public static void main(String[] args) {
double[] testData = {2,4,4,4,5,5,7,9};
StdDev sd = new StdDev();
for (double x : testData) {
sd.newNum(x);
System.out.println(sd.getSD());
}
}
public void newNum(double num) {
nums.add(num);
}
public double getAvg() {
if (nums.isEmpty()) return 0;
double ret = 0;
double sum = 0;
for (double num : nums) {
sum += num;
}
return sum / nums.size();
}
public double getSD() {
double sqDiffs = 0;
double avg = getAvg();
for (double num : nums) {
sqDiffs += (num - avg) * (num - avg);
}
return Math.sqrt(sqDiffs / nums.size());
}
}
[edit] JavaScript
Uses a closure.
function running_stddev() {
var n = 0;
var sum = 0.0;
var sum_sq = 0.0;
return function(num) {
n++;
sum += num;
sum_sq += num*num;
return Math.sqrt( (sum_sq / n) - Math.pow(sum / n, 2) );
}
}
var sd = running_stddev();
var nums = [2,4,4,4,5,5,7,9];
var stddev = [];
for (var i in nums)
stddev.push( sd(nums[i]) );
// using WSH
WScript.Echo(stddev.join(', ');
output:
0, 1, 0.942809041582063, 0.866025403784439, 0.979795897113273, 1, 1.39970842444753, 2
[edit] Liberty BASIC
Using a global array to maintain the state. Implements definition explicitly.
dim SD.storage$( 100) ' can call up to 100 versions, using ID to identify.. arrays are global.
' holds (space-separated) number of data items so far, current sum.of.values and current sum.of.squares
for i =1 to 8
read x
print "New data "; x; " so S.D. now = "; using( "###.######", standard.deviation( 1, x))
next i
end
function standard.deviation( ID, in)
if SD.storage$( ID) ="" then SD.storage$( ID) ="0 0 0"
num.so.far =val( word$( SD.storage$( ID), 1))
sum.vals =val( word$( SD.storage$( ID), 2))
sum.sqs =val( word$( SD.storage$( ID), 3))
num.so.far =num.so.far +1
sum.vals =sum.vals +in
sum.sqs =sum.sqs +in^2
' standard deviation = square root of (the average of the squares less the square of the average)
standard.deviation =( ( sum.sqs /num.so.far) - ( sum.vals /num.so.far)^2)^0.5
SD.storage$( ID) =str$( num.so.far) +" " +str$( sum.vals) +" " +str$( sum.sqs)
end function
Data 2, 4, 4, 4, 5, 5, 7, 9
New data 2 so S.D. now = 0.000000 New data 4 so S.D. now = 1.000000 New data 4 so S.D. now = 0.942809 New data 4 so S.D. now = 0.866025 New data 5 so S.D. now = 0.979796 New data 5 so S.D. now = 1.000000 New data 7 so S.D. now = 1.399708 New data 9 so S.D. now = 2.000000
[edit] lua
Uses a closure. Translation of JavaScript.
function stdev()
local sum, sumsq, k = 0,0,0
return function(n)
sum, sumsq, k = sum + n, sumsq + n^2, k+1
return math.sqrt((sumsq / k) - (sum/k)^2)
end
end
ldev = stdev()
for i, v in ipairs{2,4,4,4,5,5,7,9} do
print(ldev(v))
end
[edit] Mathematica
runningSTDDev[n_] := (If[Not[ValueQ[$Data]], $Data = {}];
StandardDeviation[AppendTo[$Data, n]])
[edit] MATLAB / Octave
The simple form is, computing only the standand deviation of the whole data set:
x = [2,4,4,4,5,5,7,9];
n = length (x);
m = mean (x);
x2 = mean (x .* x);
dev= sqrt (x2 - m * m)
dev = 2
When the intermediate results are also needed, one can use this vectorized form:
m = cumsum(x) ./ [1:n]; % running mean
x2= cumsum(x.^2) ./ [1:n]; % running squares
dev = sqrt(x2 - m .* m)
dev =
0.00000 1.00000 0.94281 0.86603 0.97980 1.00000 1.39971 2.00000
[edit] МК-61/52
0 П4 П5 П6 С/П П0 ИП5 + П5 ИП0
x^2 ИП6 + П6 КИП4 ИП6 ИП4 / ИП5 ИП4
/ x^2 - КвКор БП 04
Instruction: В/О С/П number С/П number С/П ...
[edit] Objective-C
#import <Foundation/Foundation.h>
@interface SDAccum : NSObject
{
double sum, sum2;
unsigned int num;
}
-(double)value: (double)v;
-(unsigned int)count;
-(double)mean;
-(double)variance;
-(double)stddev;
@end
@implementation SDAccum
-(double)value: (double)v
{
sum += v;
sum2 += v*v;
num++;
return [self stddev];
}
-(unsigned int)count
{
return num;
}
-(double)mean
{
return (num>0) ? sum/(double)num : 0.0;
}
-(double)variance
{
double m = [self mean];
return (num>0) ? (sum2/(double)num - m*m) : 0.0;
}
-(double)stddev
{
return sqrt([self variance]);
}
@end
int main()
{
double v[] = { 2,4,4,4,5,5,7,9 };
SDAccum *sdacc = [SDAccum new];
for(int i=0; i < sizeof(v)/sizeof(*v) ; i++)
printf("adding %f\tstddev = %f\n", v[i], [sdacc value: v[i]]);
[sdacc release];
return 0;
}
[edit] Blocks
#import <Foundation/Foundation.h>
typedef double (^Func)(double); // a block that takes a double and returns a double
Func sdCreator() {
__block int n = 0;
__block double sum = 0;
__block double sum2 = 0;
return [[^(double x) {
sum += x;
sum2 += x*x;
n++;
return sqrt(sum2/n - sum*sum/n/n);
} copy] autorelease];
}
int main()
{
NSAutoreleasePool *pool = [[NSAutoreleasePool alloc] init];
double v[] = { 2,4,4,4,5,5,7,9 };
Func sdacc = sdCreator();
for(int i=0; i < sizeof(v)/sizeof(*v) ; i++)
printf("adding %f\tstddev = %f\n", v[i], sdacc(v[i]));
[pool release];
return 0;
}
[edit] Objeck
use Structure;
bundle Default {
class StdDev {
nums : FloatVector;
New() {
nums := FloatVector->New();
}
function : Main(args : String[]) ~ Nil {
sd := StdDev->New();
test_data := [2.0, 4.0, 4.0, 4.0, 5.0, 5.0, 7.0, 9.0];
each(i : test_data) {
sd->AddNum(test_data[i]);
sd->GetSD()->PrintLine();
};
}
method : public : AddNum(num : Float) ~ Nil {
nums->AddBack(num);
}
method : public : native : GetSD() ~ Float {
sq_diffs := 0.0;
avg := nums->Average();
each(i : nums) {
num := nums->Get(i);
sq_diffs += (num - avg) * (num - avg);
};
return (sq_diffs / nums->Size())->SquareRoot();
}
}
}
[edit] OCaml
let sqr x = x *. x
let stddev l =
let n, sx, sx2 =
List.fold_left
(fun (n, sx, sx2) x -> succ n, sx +. x, sx2 +. sqr x)
(0, 0., 0.) l
in
sqrt ((sx2 -. sqr sx /. float n) /. float n)
let _ =
let l = [ 2.;4.;4.;4.;5.;5.;7.;9. ] in
Printf.printf "List: ";
List.iter (Printf.printf "%g ") l;
Printf.printf "\nStandard deviation: %g\n" (stddev l)
Sample output:
List: 2 4 4 4 5 5 7 9 Standard deviation: 2
[edit] ooRexx
sdacc = .SDAccum~new
x = .array~of(2,4,4,4,5,5,7,9)
sd = 0
do i = 1 to x~size
sd = sdacc~value(x[i])
end
say "std dev = "sd
::class SDAccum
::method sum attribute
::method sum2 attribute
::method count attribute
::method init
self~sum = 0.0
self~sum2 = 0.0
self~count = 0
::method value
expose sum sum2 count
parse arg x
sum = sum + x
sum2 = sum2 + x*x
count = count + 1
return self~stddev
::method mean
expose sum count
return sum/count
::method variance
expose sum2 count
m = self~mean
return sum2/count - m*m
::method stddev
return self~sqrt(self~variance)
::method sqrt
arg n
if n = 0 then return 0
ans = n / 2
prev = n
do until prev = ans
prev = ans
ans = ( prev + ( n / prev ) ) / 2
end
return ans
[edit] PARI/GP
Uses the Cramer-Young updating algorithm. For demonstration it displays the mean and variance at each step.
newpoint(x)={
myT=x;
myS=0;
myN=1;
[myT,myS]/myN
};
addpoint(x)={
myT+=x;
myN++;
myS+=(myN*x-myT)^2/myN/(myN-1);
[myT,myS]/myN
};
addpoints(v)={
print(newpoint(v[1]));
for(i=2,#v,print(addpoint(v[i])));
print("Mean: ",myT/myN);
print("Standard deviation: ",sqrt(myS/myN))
};
addpoints([2,4,4,4,5,5,7,9])
[edit] Perl
{
package SDAccum;
sub new {
my $class = shift;
my $self = {};
$self->{sum} = 0.0;
$self->{sum2} = 0.0;
$self->{num} = 0;
bless $self, $class;
return $self;
}
sub count {
my $self = shift;
return $self->{num};
}
sub mean {
my $self = shift;
return ($self->{num}>0) ? $self->{sum}/$self->{num} : 0.0;
}
sub variance {
my $self = shift;
my $m = $self->mean;
return ($self->{num}>0) ? $self->{sum2}/$self->{num} - $m * $m : 0.0;
}
sub stddev {
my $self = shift;
return sqrt($self->variance);
}
sub value {
my $self = shift;
my $v = shift;
$self->{sum} += $v;
$self->{sum2} += $v * $v;
$self->{num}++;
return $self->stddev;
}
}
my $sdacc = SDAccum->new;
my $sd;
foreach my $v ( 2,4,4,4,5,5,7,9 ) {
$sd = $sdacc->value($v);
}
print "std dev = $sd\n";
A much shorter version using a closure and a property of the variance:
# <(x - <x>)²> = <x²> - <x>²
{
my $num, $sum, $sum2;
sub stddev {
my $x = shift;
$num++;
return sqrt(
($sum2 += $x**2) / $num -
(($sum += $x) / $num)**2
);
}
}
print stddev($_), "\n" for qw(2 4 4 4 5 5 7 9);
- Output:
0 1 0.942809041582063 0.866025403784439 0.979795897113272 1 1.39970842444753 2
[edit] Perl 6
Using a closure:
sub sd (@a) {
my $mean = @a R/ [+] @a;
sqrt @a R/ [+] map (* - $mean)**2, @a;
}
sub sdaccum {
my @a;
return { push @a, $^x; sd @a; };
}
my &f = sdaccum;
say f $_ for 2, 4, 4, 4, 5, 5, 7, 9;
Using a state variable:
# remember that <(x-<x>)²> = <x²> - <x>²
sub stddev($x) {
sqrt
(.[2] += $x**2) / ++.[0] -
((.[1] += $x) / .[0])**2
given state @;
}
say stddev $_ for <2 4 4 4 5 5 7 9>;
- Output:
0 1 0.942809041582063 0.866025403784439 0.979795897113271 1 1.39970842444753 2
[edit] PL/I
declare A(200) float;
declare ap fixed binary;
declare i fixed binary;
ap = 0;
do i = 1 to 10;
ap = ap + 1;
get list ( A(ap) );
put skip list ( std_dev (a, ap) );
end;
std_dev: procedure (A, ap) returns (float);
declare A(*) float, ap fixed binary nonassignable;
declare i fixed binary;
declare B(ap) float, average float;
do i = 1 to ap;
B(i) = A(i);
end;
average = sum(A) /ap;
return ( sqrt (sum(B**2)/ap - average**2) );
end std_dev;
[edit] PicoLisp
(scl 2)
(de stdDev ()
(curry ((Data)) (N)
(push 'Data N)
(let (Len (length Data) M (*/ (apply + Data) Len))
(sqrt
(*/
(sum
'((N) (*/ (- N M) (- N M) 1.0))
Data )
1.0
Len )
T ) ) ) )
(let Fun (stdDev)
(for N (2.0 4.0 4.0 4.0 5.0 5.0 7.0 9.0)
(prinl (format N *Scl) " -> " (format (Fun N) *Scl)) ) )
Output:
2.00 -> 0.00 4.00 -> 1.00 4.00 -> 0.94 4.00 -> 0.87 5.00 -> 0.98 5.00 -> 1.00 7.00 -> 1.40 9.00 -> 2.00
[edit] PowerShell
This implementation takes the form of an advanced function which can act like a cmdlet and receive input from the pipeline.
function Get-StandardDeviation {
begin {
$avg = 0
$nums = @()
}
process {
$nums += $_
$avg = ($nums | Measure-Object -Average).Average
$sum = 0;
$nums | ForEach-Object { $sum += ($avg - $_) * ($avg - $_) }
[Math]::Sqrt($sum / $nums.Length)
}
}
Usage as follows:
PS> 2,4,4,4,5,5,7,9 | Get-StandardDeviation 0 1 0.942809041582063 0.866025403784439 0.979795897113271 1 1.39970842444753 2
[edit] PureBasic
;Define our Standard deviation function
Declare.d Standard_deviation(x)
; Main program
If OpenConsole()
Define i, x
Restore MyList
For i=1 To 8
Read.i x
PrintN(StrD(Standard_deviation(x)))
Next i
Print(#CRLF$+"Press ENTER to exit"): Input()
EndIf
;Calculation procedure, with memory
Procedure.d Standard_deviation(In)
Static in_summa, antal
Static in_kvadrater.q
in_summa+in
in_kvadrater+in*in
antal+1
ProcedureReturn Pow((in_kvadrater/antal)-Pow(in_summa/antal,2),0.50)
EndProcedure
;data section
DataSection
MyList:
Data.i 2,4,4,4,5,5,7,9
EndDataSection
Outputs
0.0000000000 1.0000000000 0.9428090416 0.8660254038 0.9797958971 1.0000000000 1.3997084244 2.0000000000
[edit] Python
[edit] Using a function with attached properties
The program should work with Python 2.x and 3.x, although the output would not be a tuple in 3.x
>>> from math import sqrt
>>> def sd(x):
sd.sum += x
sd.sum2 += x*x
sd.n += 1.0
sum, sum2, n = sd.sum, sd.sum2, sd.n
return sqrt(sum2/n - sum*sum/n/n)
>>> sd.sum = sd.sum2 = sd.n = 0
>>> for value in (2,4,4,4,5,5,7,9):
print (value, sd(value))
(2, 0.0)
(4, 1.0)
(4, 0.94280904158206258)
(4, 0.8660254037844386)
(5, 0.97979589711327075)
(5, 1.0)
(7, 1.3997084244475311)
(9, 2.0)
>>>
[edit] Using a class instance
>>> class SD(object): # Plain () for python 3.x
def __init__(self):
self.sum, self.sum2, self.n = (0,0,0)
def sd(self, x):
self.sum += x
self.sum2 += x*x
self.n += 1.0
sum, sum2, n = self.sum, self.sum2, self.n
return sqrt(sum2/n - sum*sum/n/n)
>>> sd_inst = SD()
>>> for value in (2,4,4,4,5,5,7,9):
print (value, sd_inst.sd(value))
[edit] Using a Closure
>>> from math import sqrt
>>> def sdcreator():
sum = sum2 = n = 0
def sd(x):
nonlocal sum, sum2, n
sum += x
sum2 += x*x
n += 1.0
return sqrt(sum2/n - sum*sum/n/n)
return sd
>>> sd = sdcreator()
>>> for value in (2,4,4,4,5,5,7,9):
print (value, sd(value))
2 0.0
4 1.0
4 0.942809041582
4 0.866025403784
5 0.979795897113
5 1.0
7 1.39970842445
9 2.0
[edit] Using an extended generator
>>> from math import sqrt
>>> def sdcreator():
sum = sum2 = n = 0
while True:
x = yield sqrt(sum2/n - sum*sum/n/n) if n else None
sum += x
sum2 += x*x
n += 1.0
>>> sd = sdcreator()
>>> sd.send(None)
>>> for value in (2,4,4,4,5,5,7,9):
print (value, sd.send(value))
2 0.0
4 1.0
4 0.942809041582
4 0.866025403784
5 0.979795897113
5 1.0
7 1.39970842445
9 2.0
[edit] R
[edit] Built-in Std Dev fn
#The built-in standard deviation function applies the Bessel correction. To reverse this, we can apply an uncorrection.
#If na.rm is true, missing data points (NA values) are removed.
reverseBesselCorrection <- function(x, na.rm=FALSE)
{
if(na.rm) x <- x[!is.na(x)]
len <- length(x)
if(len < 2) stop("2 or more data points required")
sqrt((len-1)/len)
}
testdata <- c(2,4,4,4,5,5,7,9)
reverseBesselCorrection(testdata)*sd(testdata) #2
[edit] From scratch
#Again, if na.rm is true, missing data points (NA values) are removed.
uncorrectedsd <- function(x, na.rm=FALSE)
{
len <- length(x)
if(len < 2) stop("2 or more data points required")
mu <- mean(x, na.rm=na.rm)
ssq <- sum((x - mu)^2, na.rm=na.rm)
usd <- sqrt(ssq/len)
usd
}
uncorrectedsd(testdata) #2
[edit] Racket
#lang racket
(require math)
(define running-stddev
(let ([ns '()])
(λ(n) (set! ns (cons n ns)) (stddev ns))))
;; run it on each number, return the last result
(last (map running-stddev '(2 4 4 4 5 5 7 9)))
[edit] REXX
Uses running sums.
/*REXX program to find the standard deviation of a given set of numbers.*/
parse arg # /*let the user specify numbers. */
if #='' then #=2 4 4 4 5 5 7 9 /*None given? Then use default.*/
w=words(#); s=0; ss=0 /*define: #items, a couple sums. */
do j=1 for w; _=word(#,j); s=s+_; ss=ss+_*_
say ' item' right(j,length(w))":" right(_,4),
' average=' left(s/j,12),
' standard deviation=' left(sqrt( ss/j - (s/j)**2 ),15)
end /*j*/
exit /*stick a fork in it, we're done.*/
/*──────────────────────────────────SQRT subroutine─────────────────────*/
sqrt: procedure;parse arg x; if x=0 then return 0; d=digits(); numeric digits 11; g=.sqrtGuess()
do j=0 while p>9; m.j=p; p=p%2+1; end; do k=j+5 to 0 by -1; if m.k>11 then numeric digits m.k
g=.5*(g+x/g); end; numeric digits d; return g/1
.sqrtGuess: numeric form; m.=11; p=d+d%4+2
parse value format(x,2,1,,0) 'E0' with g 'E' _ .; return g*.5'E'_%2
output using the default input
item 1: 2 average= 2 standard deviation= 0 item 2: 4 average= 3 standard deviation= 1 item 3: 4 average= 3.33333333 standard deviation= 0.942809047 item 4: 4 average= 3.5 standard deviation= 0.866025404 item 5: 5 average= 3.8 standard deviation= 0.979795897 item 6: 5 average= 4 standard deviation= 1 item 7: 7 average= 4.42857143 standard deviation= 1.39970843 item 8: 9 average= 5 standard deviation= 2
[edit] Ruby
[edit] Object
Uses an object to keep state.
"Simplification of the formula [...] for standard deviation [...] can be memorized as taking the square root of (the average of the squares less the square of the average)." c.f. wikipedia.
class StdDevAccumulator
def initialize
@n, @sum, @sumofsquares = 0, 0.0, 0.0
end
def <<(num)
# return self to make this possible: sd << 1 << 2 << 3 # => 0.816496580927726
@n += 1
@sum += num
@sumofsquares += num**2
self
end
def stddev
Math.sqrt( (@sumofsquares / @n) - (@sum / @n)**2 )
end
def to_s
stddev.to_s
end
end
sd = StdDevAccumulator.new
i = 0
[2,4,4,4,5,5,7,9].each {|n| puts "adding #{n}: stddev of #{i+=1} samples is #{sd << n}" }
adding 2: stddev of 1 samples is 0.0 adding 4: stddev of 2 samples is 1.0 adding 4: stddev of 3 samples is 0.942809041582063 adding 4: stddev of 4 samples is 0.866025403784439 adding 5: stddev of 5 samples is 0.979795897113272 adding 5: stddev of 6 samples is 1.0 adding 7: stddev of 7 samples is 1.39970842444753 adding 9: stddev of 8 samples is 2.0
[edit] Closure
def sdaccum
n, sum, sum2 = 0, 0.0, 0.0
lambda do |num|
n += 1
sum += num
sum2 += num**2
Math.sqrt( (sum2 / n) - (sum / n)**2 )
end
end
sd = sdaccum
[2,4,4,4,5,5,7,9].each {|n| print sd.call(n), ", "}
0.0, 1.0, 0.942809041582063, 0.866025403784439, 0.979795897113272, 1.0, 1.39970842444753, 2.0,
[edit] Run BASIC
dim sdSave$(100) 'can call up to 100 versions
'holds (space-separated) number of data , sum of values and sum of squares
sd$ = "2,4,4,4,5,5,7,9"
for num = 1 to 8
stdData = val(word$(sd$,num,","))
sumVal = sumVal + stdData
sumSqs = sumSqs + stdData^2
' standard deviation = square root of (the average of the squares less the square of the average)
standDev =((sumSqs / num) - (sumVal /num) ^ 2) ^ 0.5
sdSave$(num) = str$(num);" ";str$(sumVal);" ";str$(sumSqs)
print num;" value in = ";stdData; " Stand Dev = "; using("###.######", standDev)
next num
1 value in = 2 Stand Dev = 0.000000 2 value in = 4 Stand Dev = 1.000000 3 value in = 4 Stand Dev = 0.942809 4 value in = 4 Stand Dev = 0.866025 5 value in = 5 Stand Dev = 0.979796 6 value in = 5 Stand Dev = 1.000000 7 value in = 7 Stand Dev = 1.399708 8 value in = 9 Stand Dev = 2.000000
[edit] Scheme
(define ((running-stddev . nums) num)
(set! nums (cons num nums))
(sqrt (- (/ (apply + (map (lambda (i) (* i i)) nums)) (length nums)) (expt (/ (apply + nums) (length nums)) 2))))
[edit] Smalltalk
Object subclass: SDAccum [
|sum sum2 num|
SDAccum class >> new [ |o|
o := super basicNew.
^ o init.
]
init [ sum := 0. sum2 := 0. num := 0 ]
value: aValue [
sum := sum + aValue.
sum2 := sum2 + ( aValue * aValue ).
num := num + 1.
^ self stddev
]
count [ ^ num ]
mean [ num>0 ifTrue: [^ sum / num] ifFalse: [ ^ 0.0 ] ]
variance [ |m| m := self mean.
num>0 ifTrue: [^ (sum2/num) - (m*m) ] ifFalse: [ ^ 0.0 ]
]
stddev [ ^ (self variance) sqrt ]
].
|sdacc sd|
sdacc := SDAccum new.
#( 2 4 4 4 5 5 7 9 ) do: [ :v | sd := sdacc value: v ].
('std dev = %1' % { sd }) displayNl.
[edit] Tcl
[edit] With a Class
oroo::class create SDAccum {
variable sum sum2 num
constructor {} {
set sum 0.0
set sum2 0.0
set num 0
}
method value {x} {
set sum2 [expr {$sum2 + $x**2}]
set sum [expr {$sum + $x}]
incr num
return [my stddev]
}
method count {} {
return $num
}
method mean {} {
expr {$sum / $num}
}
method variance {} {
expr {$sum2/$num - [my mean]**2}
}
method stddev {} {
expr {sqrt([my variance])}
}
}
# Demonstration
set sdacc [SDAccum new]
foreach val {2 4 4 4 5 5 7 9} {
set sd [$sdacc value $val]
}
puts "the standard deviation is: $sd"
which produces the output:
the standard deviation is: 2.0
[edit] With a Coroutine
# Make a coroutine out of a lambda application
coroutine sd apply {{} {
set sum 0.0
set sum2 0.0
set sd {}
# Keep processing argument values until told not to...
while {[set val [yield $sd]] ne "stop"} {
incr n
set sum [expr {$sum + $val}]
set sum2 [expr {$sum2 + $val**2}]
set sd [expr {sqrt($sum2/$n - ($sum/$n)**2)}]
}
}}
# Demonstration
foreach val {2 4 4 4 5 5 7 9} {
set sd [sd $val]
}
sd stop
puts "the standard deviation is: $sd"
[edit] XPL0
include c:\cxpl\codes; \intrinsic 'code' declarations
int A, I;
real N, S, S2;
[A:= [2,4,4,4,5,5,7,9];
N:= 0.0; S:= 0.0; S2:= 0.0;
for I:= 0 to 8-1 do
[N:= N + 1.0;
S:= S + float(A(I));
S2:= S2 + float(sq(A(I)));
RlOut(0, sqrt((S2/N) - sq(S/N)));
];
CrLf(0);
]
Output:
0.00000 1.00000 0.94281 0.86603 0.97980 1.00000 1.39971 2.00000
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