2
$\begingroup$

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?

  • 0
    I suggest changing "sum" to "union" to make the question more readable. "Sum" had me confused for a moment.2010-11-10
  • 0
    @John done! Thank you2010-11-10
  • 0
    It may help your web search to look for "pooling" of samples, "pooled samples" or "pooled populations", and especially "pooled standard deviation".2010-11-10

2 Answers 2

3

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

0

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