LIBRARY

PRODUCTS

FORUMS

CART

Join CodeCogs

Or login with:

COST (GBP)

0.20

1.00

Statistics › Moments ›

Standard Deviation

Calculates the standard deviation of a given population.

Controller: CodeCogs

Contents

Interface
Stdev
Page Comments

Dependents

Interface

C++

Stdev

template<class T> doublestdev(	int	`n`
	T*	`data`
	bool	`total` `= false`	)

The standard deviation $\sigma$ is defined by the square root of the bias-corrected variance

$\sigma = \sqrt{ \frac {1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 }$

(1)

Physical scientists often use the term root-mean-square as a synonym for standard deviation when they refer to the square root of the mean squared deviation of a quantity from a given baseline. The standard deviation arises naturally in mathematical statistics through its definition in terms of the second central moment. However, a more natural but much less frequently encountered measure of average deviation from the mean that is used in descriptive statistics is the so-called mean deviation.

If the value of the boolean argument total is true, then the standard deviation is computed using the following formula:

$\sigma = \sqrt{ \frac {1}{N} \sum_{i=1}^N (x_i - \overline{x})^2 }$

(2)

References

MathWorld, http:mathworld.wolfram.com/StandardDeviation.html

Example 1

#include <codecogs/statistics/moments/standard_deviation.h>
#include <iostream>
int main()
{
  double x[5] = {2.5 , 6.2 , 8.0 , 9.6 , 3.8};
  double dev = Stats::Moments::stdev<double>(5, x);
  std::cout << "The population standard deviation is: " << dev << std::endl;
  return 0;
}

Output:

The population standard deviation is: 2.9192

Parameters

n	the size of the population
data	the actual population data given as an array
total	Default value = false

Returns

the standard deviation mean of a given population

Authors

Anca Filibiu (August 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

Not a member, then Register with CodeCogs. Already a Member, then Login.

Page Comments

$Peter10003\′s Photo$

Peter10003

17 Nov 11, 6:48PM

(1 reply)

How to call Stdev for buckets within a long array

I have an array of (say) 2,000 numbers,

double x[2000]={0.123, 0.2144,-9.11, ... , -0.163];

and I want to break them into buckets of 100 numbers, thus 20 buckets.

How can I invoke the Stdev routine in Objective C, so I get 20 standard deviations.

Let's also say I have a startIndex[20] that has the beginnings of each bucket, e.g. 0, 100, 200, etc. I have this, since my bucket size changes, but in this simple case: startIndex[0] = 0, startIndex[1] =100, ...,startIndex[99]=1900

Is it this?:

double stdevBucket[20];

for (int i; i<20;i++)

stdevBucket[i]=[stdev Stdev : 100 dataX:x[startIndex[i]];

$CodeCogs\′s Photo$

CodeCogs

18 Nov 11, 5:04PM

You're almost right (unless Objective C has a notation I'm not used to), so try

double stdevBucket[20];
  for(int i=0; i<20; i++)
    stdevBucket[i]= stdev(100, &dataX[i*20]);

You must login to leave a messge