A Ratio-cum-Dual to Ratio Estimator of Population Variance Using Qualitative Auxiliary Information Under Simple Random Sampling

In this paper we have proposed a class of ratio-cum-dual to ratio estimators for estimating population variance of the variable under study, using known values of some population parameters of auxiliary variable, which is available in the form of an attribute. The expressions for the bias and mean squared error of the proposed estimators have been derived upto the first order of approximation. A comparison has been made with some well known estimators of population variance available in the literature when auxiliary information is in qualitative form. It has been shown that the proposed estimator is better than the existing estimators under the optimum condition. For illustration an empirical study has been carried out.