Abstract <p>Estimating certain population characteristics has been a task for a long time and estimating the population mean has been a cornerstone among these. In this paper, some modified ratio and regression-in-ratio type estimators are proposed to estimate the population mean using robust measures of the auxiliary variable. The estimators for the single and two-phase sampling are proposed by using information on single and multiple auxiliary variables. The proposed estimators are useful when the study and auxiliary variables do not have some symmetrical distributions. The expressions for the mean square errors for the proposed estimators are obtained. The proposed estimators are compared with some available estimators. Extensive simulation studies and real data applications are done to see the performance of the proposed estimators.</p>