k-subset with maximal variance

Question

I have two versions of the same question :

1-Given a list of number (with possible duplicate ), how to find a k-subset (with possible duplicate) that maximise the variance ? is there a more efficient way than the obvious "check-all-k-subset" ?

2-Given a set of number , how do i select from that set a list of k number that maximise the variance.

Answer 1

It might be better to ask this on some Maths forum somewhere. Just a suggestion, you will get better answers there. The coding will be easy once you understand the algorithm, which is what you seem to be asking here.