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Let's say we know the standard deviation of a set of data. Furthermore, that set of data can be partitioned into subsets, and we know the standard deviation for each subset of that partition. What's the relationship between those standard deviations and the one for the whole set? Is it simple, like an average, or more complicated?

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marked as duplicate by Glen_b Jan 26 at 5:45

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  • $\begingroup$ Answered many times on site already. It's more complicated (it's easy to see that you can't just average them by simply taking a small example set of data, splitting it in two and computing the standard deviations of the whole and the two parts). You will also need the means and sample sizes of the subsets. $\endgroup$ – Glen_b Jan 26 at 5:24
  • $\begingroup$ See here for the two-variable case: en.wikipedia.org/wiki/Pooled_variance#Sample-based_statistics $\endgroup$ – Glen_b Jan 26 at 5:35