On the Arithmetic Mean Estimators of a Family of Estimators of Finite Population Variance of Ratio Type

For many years, one of the difficult components of sampling theory has been the estimation of population characteristics, especially variance. The estimation of variability is very essential in many fields (Chemistry, Biology, Mathematics, and so on) to know how one quantity varies with respect to another quantity. This paper proposes arithmetic estimators of a group of ratio estimators for populations with finite variance. Using a Taylor series technique, the bias and MSE of the proposed estimators are determined up to the first order of approximation together with the efficiency conditions over existing estimators. The effectiveness of the proposed estimators in comparison to the current estimators is evaluated using a real-world data set. The empirical findings demonstrate that the suggested estimators outperform the current estimators taken into account in the study. Hence, these suggested estimators are recommended for use in real life scenario.