Variance of superset from variance of subsets

Asked May 24 '13 at 16:06

Active May 24 '13 at 16:46

Viewed 145 times

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.

edited May 24 '13 at 16:38

asked May 24 '13 at 16:06

frickskit

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. – Glen_b May 24 '13 at 16:50
@Glen_b Would you prefer that we migrate your answer into the duplicate thread? – whuber May 24 '13 at 16:57

Variance of superset from variance of subsets

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