Given a set of N objects and associate a non-negative integer value k_i to each object in the set. Consider the following computation problem: let k'_i = \sum_i {k'_i (1/N)} = E';
Can we conclude that:
V = \sum_i {k_i^2 (1/N)} - (\sum_i {k_i (1/N)})^2 >= \sum_i {k'_i^2 (1/N)} - E'^2 =V' ?
If not, what is the relation between V and V'? I am wondering whether their relation is independent of the exact difference between k_i and k'_i, thanks!