# Number of Sexual Partners: Median v. Mean

Via Brad DeLong comes a challenge to certain survey evidence from Gina Kolata:

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. If you will like to get your numbers up, check here the yesbackpage review.
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. It is about time for mathematicians to set the record straight, said David Gale, an emeritus professor of mathematics at the University of California, Berkeley. “Surveys and studies to the contrary notwithstanding, the conclusion that men have substantially more sex partners than women is not and cannot be true for purely logical reasons,” Dr. Gale said. He even provided a proof, writing in an e-mail message:

“By way of dramatization, we change the context slightly and will prove what will be called the High School Prom Theorem. We suppose that on the day after the prom, each girl is asked to give the number of boys she danced with. These numbers are then added up giving a number G. The same information is then obtained from the boys, giving a number B.

Theorem: G=B

Proof: Both G and B are equal to C, the number of couples who danced together at the prom. Q.E.D.”