A Comparison and Contrast of Some Methods for Sample Quartiles

Abstract

A remainder representation of the sample size is exploited to write out the ranks of quartiles exhaustively which in turn help compare ranks for quartiles offered by different methods available in the literature. The criterion of equisegmentation property that the number of ranks below that of the first quartile, that between the consecutive quartiles, and that above the third quartile are the same has been used to compare. Four segmentation identities are obtained for each method of quartiles which show clearly the number of observations in each of the four quarters if the observations are distinct. The Halving Method and the Remainder Method have been proposed for the calculation of sample quartiles. Quartiles provided by each of these two methods satisfy equisegmentation property if the observations are distinct. More interestingly, these two methods provide the number of quartiles having integer ranks.