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- Combining two covariance matrices 1 answer
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.