The AM of n observations is M. If the sum of (n - 4) observations is a ,then the mean of remaining four observations is
nM−a4
nM+a2
nM−a2
nM+a
Let x1,x2,…,xn be n observations.
∴ M=x1+x2+x3+…+xnn =x1+x2+…+xn−4+xn−3+xn−2+xn−1+xn⇒nM=a+xn−3+xn−2+xn−1+xn⇒ nM−a4=xn−3+xn−2+xn−1+xn4