
Journal of Convex Analysis 24 (2017), No. 1, 199212 Copyright Heldermann Verlag 2017 Defining a Unique Median via Minimizing Families of Norms Jeffrey Tsang Dept. of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph N1G 2W1, Canada jtsang02@uoguelph.ca Rajesh Pereira Dept. of Mathematics and Statistics, University of Guelph, 50 Stone Road East, Guelph N1G 2W1, Canada pereirar@uoguelph.ca It is wellknown that the median of an even number of datapoints is not unique; by any of many equivalent definitions, any point in the interval between the innermost points qualify. Recalling that the mean can be defined by a least squares approximation to the dataset, the median via least absolute differences, we consider minimizing the L_{p} norm from the dataset to the diagonal, and compute its limit as p approaches 1 from the right side  the result is not the midpoint as typically used. We also construct a different family of strictly convex norms converging to L_{1} exhibiting a different limitmedian. [ Fulltextpdf (153 KB)] for subscribers only. 