Mathematics is fun, particularly when it messes with people's minds. Two elementary statistical-combinatorial examples from the New York Times last month illustrate:

Gina Kolata in "The Myth, the Math, the Sex" (12 Aug 2007) discusses how

... In study after study and in country after country, men report more, often many more, sexual partners than women. 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. ...

Mathematically, the mean (average) number of partners must be equal for both sexes, as various simple examples illustrate and as elementary logic proves. As originally published, however, the NYT article repeatedly confounds mean and median, perhaps due to innumeracy in the editorial process, perhaps due to authorial confusion. Nonetheless, the theorem holds.

In a subtly-related theme, John Tierney in "Is There Anything Good About Men? And Other Tricky Questions" (20 Aug 2007) begins his blog entry with:

What percentage of your ancestors were men? No, it's not 50 percent, as I'll explain shortly.

Again, this is mathematically correct — since although each person has one male parent and one female parent, the same individuals show up repeatedly in the family tree once one goes back a few generations — and more of the duplicates are on the male side. Empirically, humans on the average seem to have about twice as many distinct female ancestors than male ancestors, based on genetic analysis. It's all related to the hugely-greater variance in reproductive success of males ...

(cf. HatProblem (26 Jul 2003), BadArithmetic (24 Feb 2004), ...)

TopicScience - TopicHumor - 2007-09-18

(correlates: Comments on UncleBert, HardCoreBelievers, 2004-11-06 - Fallen Leaf Forest Floor, ...)