The Median Is the Message : toward the Fréchet Median

One could argue that the long-standing controversy over the relative merits of the median and mean is something of a touchstone of early statistics. The touchstone of medieval alchemy was basonite, a variety of quartz used to test the purity of gold alloys ; striking an alloy against the surface of the stone revealed the quality of the alloy by the color of the mark left on the stone. Likewise, reading the marks left by Laplace, Edgeworth, Fisher, Fréchet, Kolmogorov, Tukey and Huber on the merits of the median all reveal a noble quality of mind, or perhaps instead just a mutual willingness to come to the aid of the statistically maligned and downtrodden. 1 Fréchet’s case for the median, reviewed in his reprinted 1940 article and prefigured in his earlier work, Fréchet (1924, 1935), was only part of a much wider campaign he waged beginning in the mid-1920’s against the misuse of the coefficient of correlation. The idea that simplistic models of linear relationships for conditional means could capture all the subtleties of stochastic dependence seemed quite absurd, and the prevailing notion, particularly in the social sciences, that causality could be reduced to the