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.


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