Extreme-cum-median ranked set sampling has been developed to address the problem of heterogeneity and outliers / extreme values. Double ranked set sampling has been suggested to obtain more reliable samples using the concept of degree of distinguishability. Dealing with heterogeneous and non-normal populations seems to be an area with a dearth of research. This article endeavors to address this research gap by introducing a new, improved ranked set sampling procedure that combines the aforementioned approaches, which is called double extreme-cum-median ranked set sampling. A simulation study for some symmetric and asymmetric probability distributions has been conducted. The results show that the newly proposed scheme performs better than its competitors under perfect and imperfect ranking, but the best performance has been observed for Weibull distribution with perfect ranking. An empirical study utilizing real-life data following skewed distribution was carried out. The real-life data results align well with the Monte Carlo simulation outcomes. Due to its flexible ranking options, the newly proposed technique is suggested for heterogeneous and non-normal populations.