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A new modification of ranked set sampling (RSS) is investigated to estimate the mean of the study population. This modified approach is a double-stage approach and a kind of combination between RSS and median RSS (MRSS). It is shown that this new modification is more efficient than of RSS, MRSS, and simple random sampling. The Hellinger distance is used to show that the new approach is more practical than any other double-stage RSS., REVSTAT-Statistical Journal, Vol. 19 No. 1 (2021): REVSTAT-Statistical Journal