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Extensive research work has been done for the estimation of population mean using bivariate auxiliary information based on conventional measures. Conventional measures of the auxiliary variables provide suspicious results in the presence of outliers/extreme values. However, non-conventional measures of the auxiliary variables include quartile deviation, mid-range, inter-quartile range, quartile average, tri-mean, Hodge-Lehmann estimator etc. give efficient results in case of extreme values. Unfortunately, non-conventional measures are not used by survey practitioners to enhance the estimation of unknown population parameters using bivariate auxiliary information. In this article, difference-cum-exponential-type estimators for population mean utilizing bivariate auxiliary information based on non-conventional measures under simple and stratified random sampling schemes have been suggested. Mathematical properties such as bias and mean squared error are derived. To support theoretical findings, various real-life applications are used to confirm the superiority of the suggested estimators as compared to the competing estimators under study. [ABSTRACT FROM AUTHOR]