A New Look at Quartiles of Ungrouped Data

Traditional methods of calculation of quartiles for ungrouped data are based on interpolation. In this article we focus on three methods of defining measures of this kind. Then we present hinges that divide data into four parts by a lower hinge, a median, and an upper hinge. A hinge is “crudely, a quartile.” The preceding four techniques may yield different numerical answers when applied to the same set of data. Two tests are proposed and are used to evaluate the various methods for calculation of quartiles and hinges. Finally, an alternative method of calculating quartiles is provided; it retains desirable characteristics of quartiles and combines them with the advantages ascribed to hinges.