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This question already has an answer here:

Let's say I want to estimate $var(A)$ of a list of numbers $a_i \in A, i\in [0,N]$.

However, I only have the variance of the non-overlapping, and complete ($B \cup C = A)$ subsets $B$ and $C$.

Assume $B$ contains all $a_i \in [0, N/2]$ and $C$ contains all $a_i \in [N/2, N]$

How can I find $var(A)$ from $var(B)$ and $var(C)$

Note: obviously I do not have the list of numbers in $B$ and $C$, but you can assume that I know the size of each (and, if necessary the mean of each).

If it's not possible, please try to tell me why.

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marked as duplicate by whuber May 24 '13 at 16:37

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Actually, see the edit in this answer, which does it; it just took a while to find a good one. I'll delete my answer in a few minutes. $\endgroup$ – Glen_b May 24 '13 at 16:50
  • $\begingroup$ @Glen_b Would you prefer that we migrate your answer into the duplicate thread? $\endgroup$ – whuber May 24 '13 at 16:57