# ds_list_variance

In probability theory and statistics, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical. Variance is always non-negative: a small variance indicates that the data points tend to be very close to the mean (expected value) and hence to each other, while a high variance indicates that the data points are very spread out around the mean and from each other.

Population Variance

In general, the population variance of a finite population of size $$N$$ with values $$x_i$$ is given by

$$\sigma^2 = \frac 1N \sum_{i=1}^N \left(x_i - \mu \right)^2$$

where

$$\mu = \frac 1N \sum_{i=1}^N x_i$$

is the population mean.

ds_list_variance(id[,sample])
Returns the variance of the values in a given list.
COPY/// ds_list_variance(id[,sample])
//
//  Returns the variance of the values in a given list.
//
//      id          list data structure, real
//      sample      true if the list is made up of a sample, bool
//
{
var n, avg, sum, i;
n = ds_list_size(argument0);
avg = 0;
sum = 0;

for (i=0; i<n; i+=1) avg += ds_list_find_value(argument0, i);
avg /= n;
for (i=0; i<n; i+=1) sum += sqr(ds_list_find_value(argument0, i) - avg);

return sum/(n - argument1);
}


Contributors: Quimp

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