In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

In this study, we introduced a novel generalized class of ratio-type estimators for median estimation by employing quantile regression within the framework of neutrosophic statistics is designed to enhance the accuracy and reliability of estimates in the presence of data uncertainty, providing a robust alternative to traditional point estimators. The proposed methodology yields interval-based estimates for the population median, capturing a range of possible values rather than a point estimate, which allows modeling uncertainty and partial truth inherent in complex or imprecise data. This is achieved within the neutrosophic statistical framework, a generalization of classical statistics that explicitly accounts for indeterminacy and inconsistent information, making it well-suited for handling ambiguous data in interdisciplinary applications. We validate the performance of our estimators using real-life stock price data from Samsung Electronics Co. Ltd. (SMSN.IL), sourced from Yahoo Finance (2022), and further substantiate the results through a comprehensive simulation study. Comparisons between traditional and proposed estimators, based on mean squared error, percentage decrease in mean squared error, and a simulation study, demonstrate the superior precision and reliability of our approach.