Letbe a random id algebraic polynomial where {ai} 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 Qn(x). We have shown that the bound isfor sufficiently large n. Our estimate istimes that of Maslova (1974). We have also presented a graph and a comparison table illustrating the values of variances