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ds_list_standard_score

Wikipedia:

In statistics, the standard score is the (signed) number of standard deviations an observation or datum is above the mean. Thus, a positive standard score indicates a datum above the mean, while a negative standard score indicates a datum below the mean. It is a dimensionless quantity obtained by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.

The standard score of a raw score x is

$$\large z = {x- \mu \over \sigma}$$

where: \(\mu\) is the mean of the population; \(\sigma\) is the standard deviation of the population

ds_list_standard_score(id,pos)
Returns the standard score (z-score) of the value at a given position in a given list.
COPY/// ds_list_standard_score(id,pos)
//
//  Returns the standard score (z-score) of the 
//  value at a given position in a given list.
//
//      id          list data structure, real
//      pos         position in the list, real
//
/// GMLscripts.com/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 (ds_list_find_value(argument0, argument1) - avg)/sqrt(sum/n);
}

Contributors: Quimp

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