Suppose in a plane, there is a set of points, whose distance to $(0,0)$ is always 1:
Each point is assigned with a weight (possible negative):
$[w(0,1) = 1, w(1,0) = 2,w(0.707,0.707) = -1,w(0.707,-0.707)= -2,...]$
Suppose the standard deviation of the points are defined as the top answer here: https://stats.stackexchange.com/questions/13272/2d-analog-of-standard-deviation
Find a subset of points $S$ such that SUM(w)×STD is maximized.
My gut feeling is that this problem is NP hard. Very similar to knapsack problem. However, knapsack use weight as a threshold. I'm not sure how to transfer the standard deviation here. Any thought on how to prove this would be appreciated!