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

Towards the Efficiency of the Ratio Estimator for Population Median in Survey Sampling Matthew Joshua Iseh Absract- This study leveraged on the fact that researchers in survey sampling so metimes do not take into c onsideration the tool that will be most appropriate in the measure of location. As a result, users of statistics often go for the mean or total, which has been widely discussed in the finite population sampling literature, unlike the median, which is more complicated to deal with given that it has to do with ordered data. This study suggests an estimator of population median in single and double sampling technique with two auxiliary variables. From the result obtained, it is established that the proposed estimators perform better when the considered variables are from a highly skewed distribution, such as income, expenditure, scores. In addition, it was observed that the proposed estimators were less bias and more efficient than the existing estimators of their class. I. I ntroduction Most times in survey sampling, some researchers do not take into consideration the tool that will be most appropriate in the measure of location. As a result, users of Statistics often go for the mean or total which has been widely discussed in the finite population sampling literature unlike the median which is more complicated to deal with since it has to do with ordered data. However, it has been established that the median unlike the mean performs better when the considered variables are from a highly skewed distribution. In surveys involving the estimation of income, expenditure, scores, etc., it is very reasonable to assume that the population median unlike the population mean is known, hence the possibility of incorporating auxiliary information in the formulation of such estimators. Authors like Gross (1980), Kuk and Mak (1989), Singh et al. (2003), Singh and Solanki (2013), Aladag and Cingi (2015), have made useful contributions in estimation of population median. Works by Enang et.al . (2016) on alternative exponential median estimator, Shabbir, and Gupta (2017) on a generalized difference type estimator for population median and Iseh (2020)on enhancing efficiency of ratio estimator of population median by calibration techniques were added advantage in this area. However, it should also be noted that not much has been done in estimating population median.On further improvement of the median estimator, Singh, Joarder, and Tracy (2001), extended the ratio estimator to two-phase sampling, whileSingh, Singh, and Upadhyaya (2007) suggested the ratio-type estimator in two-phase sampling using two auxiliary variables. In addition, Jhajj, Kaur, and Jhajj (2016), defined a ratio exponential-type estimator in two phase sampling with two auxiliary variables. On the lines of Shabbir and Gupta (2017), Baig, Masood and Tarray (2019) suggested an Author: Ph.D., Department of Statistics, AkwaIbom State University, MkpatEnin, Nigeria. e-mail: eeseaglechild@gmail.com 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 37 ( F ) © 2021 Global Journals Version I N otes