Assuming I have a set of values called S and the STD of S is Xs. Let's say I split S into two subsets S1 and S2 with standard deviations X1 and X2. The number of elements in S1 and S2 are called W1 and W2. So my question is, assuming I have the values for X1, X2, W1, and W2; is it possible to figure out what Xs is?
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Its not possible to get the sample standard deviation from the standard deviations and sizes of a partition, you also need to know the mean of each partition. Otherwise, what happens if the means of each parition are very far apart? The variance of the whole sample will be much greater than the apparent variation of each partition.
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So even if I have the mean of the partitions its still not possible? – Jose Martinez Dec 05 '13 at 21:29
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No if you know the partition means then you can reconstruct the sample standard deviation – Dec 05 '13 at 22:18