Let   be a random id algebraic polynomial where a_i is a sequence of independent identically distributed ( iid ) standard normal random variables. In this paper we have obtained a lower bound for the variance of the number of real zeros .of the random algebraic polynomials Q_n(x). We have shown that the bound is   for sufficiently large n. Our estimate is  times that of Maslova (1974). We have also presented a graph and a comparison table illustrating the values of variances