Variance Estimation Using Median of the Auxiliary Variable

The present paper deals with a modified ratio type variance estimator for estimation of population variance of the study variable, when the population median of the auxiliary variable is known. The bias and the mean squared error of the proposed estimator are obtained and also derived the conditions for which the proposed estimator performs better than the traditional ratio type variance estimator suggested by Isaki10 and the modified ratio type variance estimators suggested by Kadilar and Cingi11. Further we have compared the efficiencies of the proposed estimator with that of traditional ratio type variance estimator and existing modified ratio type variance estimators for certain known populations. From the numerical study it is observed that the proposed estimator performs better than the traditional ratio type variance estimator and existing modified ratio type variance estimators.