What are the advantages of combined variance?

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## Charu

Like combined mean, the combined variance or standard deviation can be calculated for different sets of data. Suppose we have two sets of data containing n1 and n2 observations with means X¯¯¯¯1 and X¯¯¯¯2 and variances S12 and S22. If X¯¯¯¯c is the combined mean and Sc2 is the combined variance of n1+n2 observations, then combined variance is given by:

Sc2=n1S12+n2S22+n1(X¯¯¯¯1–X¯¯¯¯c)2+n2(X¯¯¯¯2–X¯¯¯¯c)2n1+n2