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

I: Baig, Masood and Tarray (2019) suggested an improved class of difference-type estimators for population median using two auxiliary variables � = � � + 1 � − � �� � 2 � − � + � � + (1 − 2 ) � � − + � �� Where 1 and 2 are unknown constant. � � � = � 1 � 2 − 1 2 � + � 1 2 − 2 �� where 1( ) = � − � �1− 2 � and 2( ) = � 2 −1 � +2 � − � 2 � 2 −1� � � � = 2 2 �1− 2 � ��1 − 2 − 2 − 2 + 2 �� (9) III. T he P roposed E stimator under S imple R andom S ampling with O ne V ariable � ( ) = � � � + (1 − ) � � � ( − � ) ( + � ) � (10) � ( ) = (1 + 0 )[1 + 1 − 2 1 + 12 ] � − 1 2 �1 − 1 2 + 12 4 �� � ( ) = �1 + 0 + � 1 2 − 2 � 1 + � 1 2 − 2 � 0 1 + �2 − 1 8 � 12 � � ( ) − = � 0 + � 1 2 − 2 � 1 + � 1 2 − 2 � 0 1 + �2 − 1 8 � 12 � (11) � � ( )� = ��2 − 1 8 � 2 + � 1 2 − 2 � � (12) Squaring both sides of (11), retaining terms to the second-degree and taking expectations, the MSE of � ( ) to the first order of approximation is obtained as; � � ( )� = 2 � 2 + � 1 2 − 2 � 2 2 + 2 � 1 2 − 2 � � (13) minimizing (13) with respect to gives = 2 1 +1 4 � � ( )� = 2 2 (1 − 2 ) (14) 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 4 ( F ) © 2021 Global Journals Version I N otes