(PECL stats >= 1.0.0)
stats_standard_deviation — Returns the standard deviation
$a
[, bool $sample = false
] )
aThe array of data to find the standard deviation for. Note that all values of the array will be cast to float.
sample
Indicates if a represents a sample of the
population; defaults to FALSE.
Returns the standard deviation on success; FALSE on failure.
Raises an E_WARNING when there are fewer than 2
values in a.
If you don't have the stat package you can use these functions:
<?php
// Function to calculate square of value - mean
function sd_square($x, $mean) { return pow($x - $mean,2); }
// Function to calculate standard deviation (uses sd_square)
function sd($array) {
// square root of sum of squares devided by N-1
return sqrt(array_sum(array_map("sd_square", $array, array_fill(0,count($array), (array_sum($array) / count($array)) ) ) ) / (count($array)-1) );
}
?>
Here's an implementation that adheres to the PECL source quite strictly. This is useful for people who want to use it but don't have the extension, as well as for people who want to understand what is going on.
<?php
if (!function_exists('stats_standard_deviation')) {
/**
* This user-land implementation follows the implementation quite strictly;
* it does not attempt to improve the code or algorithm in any way. It will
* raise a warning if you have fewer than 2 values in your array, just like
* the extension does (although as an E_USER_WARNING, not E_WARNING).
*
* @param array $a
* @param bool $sample [optional] Defaults to false
* @return float|bool The standard deviation or false on error.
*/
function stats_standard_deviation(array $a, $sample = false) {
$n = count($a);
if ($n === 0) {
trigger_error("The array has zero elements", E_USER_WARNING);
return false;
}
if ($sample && $n === 1) {
trigger_error("The array has only 1 element", E_USER_WARNING);
return false;
}
$mean = array_sum($a) / $n;
$carry = 0.0;
foreach ($a as $val) {
$d = ((double) $val) - $mean;
$carry += $d * $d;
};
if ($sample) {
--$n;
}
return sqrt($carry / $n);
}
}
?>
If you want one function for the population and sample, you can use this function:
<?php
function standard_deviation($aValues, $bSample = false)
{
$fMean = array_sum($aValues) / count($aValues);
$fVariance = 0.0;
foreach ($aValues as $i)
{
$fVariance += pow($i - $fMean, 2);
}
$fVariance /= ( $bSample ? count($aValues) - 1 : count($aValues) );
return (float) sqrt($fVariance);
}
Function to calculate square of value - mean
<?php
function sd_square($x, $mean) { return pow($x - $mean,2); }
?>
Function to calculate standard deviation (uses sd_square)
<?php
function sd($array) {
// square root of sum of squares devided by N-1
return sqrt(array_sum(array_map("sd_square", $array, array_fill(0,count($array), (array_sum($array) / count($array)) ) ) ) / (count($array)) );
}
?>
works better if you don't add +1 to the count
standard deviation of a constant must be 0 ( http://en.wikipedia.org/wiki/Standard_deviation )
different way :
<?php
class Tmath{
public static function variance($data, $round = 2)
{
if( count($data) == 0 )
return NULL;
$total_ecart = 0;
$moyenne = self::moyenne($data, 10*$round);
if( $moyenne == 0)
return 0;
foreach( $data as $element)
{
$total_ecart += pow($element, 2);
}
return round($total_ecart/count($data) - pow($moyenne,2),$round);
}
public static function ecartType($data, $round = 2)
{
return round(sqrt(self::variance($data,10*$round)),2);
}
public static function moyenne($data, $round = 2)
{
if( count($data) == 0 )
return NULL;
return round(array_sum($data)/count($data),$round) ;
}
}
?>
It should be known that this function also casts all of the values of the array to floats. If you pass an array of integers, they will come out as an array of floats.
$data = array(2,3,3,3,3,2,5);
var_dump($data);
$standardDeviation = stats_standard_deviation($data);
var_dump($data);
Prints:
array
0 => int 2
1 => int 3
2 => int 3
3 => int 3
4 => int 3
5 => int 2
6 => int 5
array
0 => float 2
1 => float 3
2 => float 3
3 => float 3
4 => float 3
5 => float 5
6 => float 2
