Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

Population 4: Let as the U.S. exports to Singapore in billions of Singapore dollars, as the money supply figures in billions of Singapore dollars and is the local supply in U.S. dollars given by Aczel and Sounder pandian (2004). = 67 ; ′ = 23 ; = 15 ; = 4.8 ; = 70 ; = 151 ; = 0.6624 ; = 0.7592 ; = 0.8624 ; ( ) = 0.0763 ; ( ) = 0.0526 ; and ( ) = 0.0024 ; Population 5: Let be the district-wise tomato production (tones) in 2 03, as a district-wise tomato production (tones) in 2002 and as a district-wise tomato production (tones) in 2001 given by MFA (2004). From the numerical study of three real life data sets, the following remarks are deduced; Table 2: Results for Two Phase Sampling Population III Population IV Population V Estimator AB MSE PRE AB MSE PRE AB MSE PRE � 0 346606 100 0 1.23 100 0 64795.1 100 � 0 729125.3 47.54 0.00 1.89 65.08 0 146126.9 44.3 � 58.72 391934.3 88.43 0.35 -85.12 -1.45 8.49 69573.62 93.1 � 259.20 363711.8 95.30 0.09 -85.60 -1.44 286.51 70062.2 92.5 � 32818.5 294885.2 117.54 1.21 0.01 12300 894.49 65213.1 99.4 � ( ) 8.20 310481.2 111.64 0.07 0.29 424.14 8.57 84943.4 76.3 N/B: AB=Absolute bias IV. D iscussion From the result in Table 1, it is observed that the proposed estimator � ∗ ( ) has outperformed other existing estimators considered in this study and as a result considered the more preferred estimator with respect to this set of data. However, the existing estimator � had greater efficiency but heavily biased in both population I and II respectively. Again, as shown in Table 2, the proposed estimator � ( ) has an overwhelming performance in terms of higher gains in efficiency and minimum bias as compared to the existing estimators considered in this study. This superiority in the gain in efficiency and minimum bias of the proposed estimator is because of the endearing properties of the separate ratio product – type estimator. However, � , notice ably from population III, IV, and V had slight gain in efficiency over the proposed estimator but highly biased, and not recommended for estimation of population median. It is important to note that, although the existing estimator � is asymptotically unbiased from the sets of data considered in this study, it was less efficient, and should not form a bet for median estimation. It becomes imperative to seek for an estimator that isless bias with minimum MSEthat will enhance the Towards the Efficiency of the Ratio Estimator for Population Median in Survey Sampling 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 47 ( F ) © 2021 Global Journals Version I = 97 ; ′ = 46 ; = 33 ; = 1242 ; = 1233 ; = 1207 ; = 0.2096 ; = 0.15 ; = 0.123 ; ( ) = 0.00021 ; ( ) = 0.0002 ; and ( ) = 0.0002 ; N otes