Advanced class for variance estimation utilising known quartiles of the auxiliary variable

Variance is a natural phenomenon among similar objects in nature and it is one of the measures of dispersion. Therefore, its estimation is of crucial importance for large populations to save time, money and manpower. In this paper, we propose an estimator for estimating population variance of the primary (study) variable using known quartiles of the secondary (auxiliary) variable and their functions. The optimum value of the scalar in the suggested estimator is acquired to ensure mean squared error (MSE) of the suggested estimator as a minimum. A comparison has been presented between suggested and the competing estimators, and the theoretical efficiency conditions are derived. For the verification of these efficiency conditions through the calculation of mean square errors of various estimators, a numerical study is performed.