How do I determine the standard deviation (stddev) of a set of values?

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While the sum of squares algorithm works fine most of the time, it can cause big trouble if you are dealing with very large numbers. You basically may end up with a negative variance…

Plus, don’t never, ever, ever, compute a^2 as pow(a,2), a * a is almost certainly faster.

By far the best way of computing a standard deviation is Welford’s method. My C is very rusty, but it could look something like:

public static double StandardDeviation(List<double> valueList)
{
    double M = 0.0;
    double S = 0.0;
    int k = 1;
    foreach (double value in valueList) 
    {
        double tmpM = M;
        M += (value - tmpM) / k;
        S += (value - tmpM) * (value - M);
        k++;
    }
    return Math.Sqrt(S / (k-2));
}

If you have the whole population (as opposed to a sample population), then use return Math.Sqrt(S / (k-1));.

EDIT: I’ve updated the code according to Jason’s remarks…

EDIT: I’ve also updated the code according to Alex’s remarks…

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