The average of n numbers x1,x2,x3,…,xn is M. If xn is replaced by x', then new average is

M=x1+x2+x3……xnn⇒ nM=x1+x2+x3+…+xn−1+xn⇒ nM−xn=x1+x2+x3+…+xn−1⇒ nM−xn+x′=x1+x2+x3+…+xn−1+x′⇒ nM−xn+x′n=x1+x2+x3+…+xn−1+x′n∴  New average =nM−xn+x′n