ds_list_variance

Wikipedia:

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
//
/// gmlscripts.pro/license
{
    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

Related: ds_list_add_list, ds_list_add_map, ds_list_cv, ds_list_flip, ds_list_geometric_mean, ds_list_load, ds_list_max, ds_list_mean, ds_list_median, ds_list_min, ds_list_pop_standard_deviation, ds_list_range, ds_list_save, ds_list_select_relative, ds_list_select_relative_wrap, ds_list_standard_deviation, ds_list_standard_score, ds_list_sum, ds_list_sum_squares, ds_list_variance, ds_list_vmr

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