A new generalised median-based estimator of the finite population mean

To enhance the performance of an estimator, the use of additional information on study variables instead of the auxiliary variables may be a good alternative in survey sampling as it does not increase the survey cost. One of the examples of such additional information is the use of the median of the main variable. There is no need for full information on units of the population under consideration for the median, so many times it is known to us. In the present article, we have developed an extended ratio estimator for the population mean utilising a given population median of the study variable. We have driven out the expressions for bias of suggested estimator along with its MSE up to the approximation of degree one. The optimal value of the characterising scalar has also been derived using the method of maxima and minima. The conditions under which the suggested estimator is more efficient than previous estimators are also obtained. Our findings, in theory, are supported by the numerical illustration consisting of three different natural populations. The efficiency of the suggested estimator over competing estimators is also presented in the form of graphical representation.