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# Variance

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Calculates the variance of a given set of data.
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Contents

C++

## Variance

 template doublevariance( int n T* data bool total = false )
Consider a discrete random variable . The variance  of is defined as


Note that  is a new random variable (it's a function of  ). The variance is also denoted as . A useful formula that follows inmediately from the definition is that


In words, the variance of  is the second moment of  minus the first moment squared. The variance of a random variable determines a level of variation of the possible values of  around its mean. However, as this measure is squared, the standard deviation is used instead when one wants to talk about how much a random variable varies around its expected value.

If we cannot analyze a whole population but we have to take a sample, we define its variance (denoted as ) with the formula:



where  is the aritmetic mean . The value for  is an estimator for . \[]

If the value of the boolean argument <em> total </em> is true, then the variance is computed using the following formula:


## References:

PlanetMath, http:planetmath.org/encyclopedia/Variance.html

### Example 1

#include <codecogs/statistics/moments/variance.h>
#include <iostream>
int main()
{
int x[5] = {3 , 1 , 5 , 6 , 9};
double var = Statistics::Moments::variance<int>(5, x);
std::cout << "The population variance is: " << var << std::endl;
return 0;
}
Output:
The population variance is: 9.2

### Parameters

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

### Returns

return value the variance of the given set of data

### Authors

Anca Filibiu (August 2005)
##### Source Code

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

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