The Media and the Median (Fallacy Files)

Fallacy Files points out an amusing error in a recent New York Times science article, "The Myth, The Math, The Sex" by Gina Kolata. The article states:

"One survey, recently reported by the federal government, concluded that men had a median of seven female sex partners. Women had a median of four male sex partners. Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes and women had 6.5.

But there is just one problem, mathematicians say. It is logically impossible for heterosexual men to have more partners on average than heterosexual women. Those survey results cannot be correct."

However, as Fallacy Files points out, even in a population of equal numbers of men and women over a given time period, the median number of sex partners could be different. All you need are a few very active women who raise the mean a lot but don't raise the median too much (Madonna-whore dichotomy?). From Fallacy files:

"It's discouraging that an article this innumerate would be published in the Times, and I suppose that the mathematician quoted was not the source of the confusion, but that it must have been introduced in the writing or editing. As it is, there's no evidence in the article of anything impossible in the statistics cited. A British survey is quoted, but the article doesn't indicate whether the numbers are medians, means, or what―which is a problem in itself!

Moreover, the article presents itself as busting the "myth" that heterosexual men are more promiscuous than heterosexual women. Surely, the "myth" is that the typical man has more sex partners than the typical woman. In order for this to be true, there must be some atypically promiscuous women. Whether the "myth" is true or not, I don't know―damn it, Jim, I'm a logician, not a sociologist!―but I do know that it is an empirical question and not a logical or mathematical one."