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javastatisticsapache-commons

apache-commons DescriptiveStatistics gives wrong StandardDeviation?

I have this code:

    DescriptiveStatistics stats = new DescriptiveStatistics( new double[] {2,4,4,4,5,5,7,9} );
    System.out.println("var="+stats.getVariance());
    System.out.println("sd="+stats.getStandardDeviation());

I took the example from Wikipedia https://en.wikipedia.org/wiki/Standard_deviation. The answer should be var=4.0, sd=2.0, but what I get is:

    4.571428571428571
    2.138089935299395

What am I missing?

Solution

  • getVariance() divides by n-1, here from the docs:

    Returns the (sample) variance of the available values.

    This method returns the bias-corrected sample variance (using n - 1 in the denominator). Use getPopulationVariance() for the non-bias-corrected population variance.

    Background: typically, one has a sample from the population, and by calculating the bias-corrected (or unbiased) sample variance, the expected value of the calculated estimate equals the population variance. I wrote sample code that demonstrates this for this answer. And Wikipedia has background on population variance vs. sample variance.