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When I see your blog, I look 'Top contributors' list immediately. And I saw you are not first..
stop it already
You said "let's assume we'll pick an odd-sized subset for now" and forgot to prove why it's optimal.
You're right, thanks for pointing this out! It's not necessarily optimal, one has to consider the even-sized subsets as well, but the solution is really similar for that case so I don't think digging into it would add much now :)
Actually in that problem one may prove that even-size subset can always be replaced with an odd-size subset without making the simple skewness smaller. Just consider removing the second middle element from the set.