If a variable takes values 0,1,2,…,n with frequencies 1,nC1,nC2,…,nCn then the AM is

The required mean is given by X¯=0⋅1+1⋅nC1+2⋅nC2+3⋅nC3+…+n⋅nCn1+nC1+nC2+…+nCnX¯=∑r=0n r⋅nCr∑r=0n nCr=∑r=1n r⋅nrn−1Cr−1∑r=0n nCr=n∑r=1n n−1Cr−1∑r=0n nCrX¯=n×2n−12n=n2`