Imagine I had two sets of samples. The only information I have about them is their
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?
On
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:
http://upload.wikimedia.org/math/9/5/1/951ab01cabd025deadd5bf497bae971f.png
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