# Is it possible to calculate the standard deviation without the samples?

Imagine I had two sets of samples. The only information I have about them is their

• Size
• Average
• Standard deviation

Is it possible to calculate the standard deviation of a third set that is composed by the union of all samples in both sets? And what if the original sets had the same size?

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I suggest changing "sum" to "union" to make the question more readable. "Sum" had me confused for a moment. –  John D. Cook Nov 10 '10 at 16:47
@John done! Thank you –  Jader Dias Nov 10 '10 at 17:03
It may help your web search to look for "pooling" of samples, "pooled samples" or "pooled populations", and especially "pooled standard deviation". –  T.. Nov 10 '10 at 22:21

Yes, it is possible. The equation should be in your book, or you can look at the Wikipedia page under the heading Population-based statistics

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As Ross suggested, from Wikipedia:

Standard deviations of non-overlapping (X ∩ Y = ∅) sub-populations can be aggregated as follows if the size (actual or relative to one another) and means of each are known: