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I think it is not easy (at least for me) to formulate the deviation part, so let's omit it... Let decision variable $b_i = 1$ if $x_i$ is chosen, otherwise $b_i = 0$. The mean value is defined by $$\sum b_i \bar{X} = \sum b_ix_i.$$ To vanish the bilinear term, introduce new variables $y_i$, to ensure $$y_i = b_i\bar{X},$$ introduce constraints  -Mb_i \...