Question

If mean of a set of observations is x bar, then evaluate sigma(xi-x bar).

Answer 1

sigma (i =0 to n) (xi - xbar) 
= sigma (i =0 to n) xi - sigma (i = 0 to n) xbar 
= sigma (i =0 to n) xi - (n + 1)*xbar, since xbar is constant 
= sigma (i =0 to n) xi - (n + 1)*[sigma (i =0 to n) xi]/(n + 1), from definition of the mean 
= sigma (i =0 to n) xi - sigma (i =0 to n) xi 
= 0