s^2 =  \sum{i=1, n}(a_i^2-2a_ix+x^2)/n
= (\sum{i=1, n} a_i^2 - 2x \sum{i=1, n} a_i + nx^2)/n
= \sum{i=1, n} a_i^2/n - 2x^2 + x^2
= \sum{i=1, n} a_i^2/n - x^2 ................................................ IMPORTANT!
= \sum{i=1, n} a_i^2/n - (\sum{i=1, n} a_i)^2/n^2


Notice that :
For b_i = a_i + d

s^2(b) = s^2(a)-

