Given a finite set defined in real number $\{x \mid 0< x < 1 \}$ with size $N > 3$
If I split $\{x\}$ into two subsets $\{A\}$ and $\{B\}$ , $A\cup B = X$ and $A\cap B = \emptyset $, How can i find the special subsets, which have maximum $Std(A)+Std(B)$.
${\displaystyle Std={\sqrt {\frac {\sum _{i=1}^{N}(x_{i}-{\overline {x}})^{2}}{N-1}}}.}$