Setting aside gay relationships, who has sex more?  Men or woman?

Most polls and studies show what you probably already believe: men have more sex partners than woman.

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, wait a second…

How can this be? asks the very smart people:

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.

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“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.”

Sex survey researchers say they know that Dr. Gale is correct. Men and women in a population must have roughly equal numbers of partners. So, when men report many more than women, what is going on and what is to be believed?

“I have heard this question before,” said Cheryl D. Fryar, a health statistician at the National Center for Health Statistics and a lead author of the new federal report, “Drug Use and Sexual Behaviors Reported by Adults: United States, 1999-2002,” which found that men had a median of seven partners and women four.

But when it comes to an explanation, she added, “I have no idea.”

Oh, dear.  Too bad these smart people don’t know the difference between a median and an average.

An average is also known as a mean.  The mean is determined by totalling the numbers of your set, and then dividing by the number of samples.

For example, let’s say that John had sex with 6 women, Barry had sex with 2 women, Gordon had sex with 12 women, and both Carl and Lenny have never had sex with a woman. 

The AVERAGE?  (6 + 7 + 12 + 0 +0) divided by 5, which is equal to five.

The median, however, is something else.  It is the number in the middle of your sample.  In the case, about, the median is seven (there are two numbers higher and two numbers lower).

Now, we would expect that the AVERAGE number of men sleeping with women to be the same as the AVERAGE number of women sleeping with me.  But the studies mentioned in the article talk about medians.  And there is no reason to believe that the distribution curve of men is the same as that of women.

It’s a shame that none of these "mathematicians" or "statisticians" picked up on this important difference.  (Or perhaps, the New York Times author of this article simply screwed up).

The real facts are probably this:  YES, on AVERAGE, men have just as many sex partners as women.  But the distribution of those two genders — men and women — are different, which is why they have different medians.

(Another reason: men might be more inclined to exaggerate their numbers, while women might be more inclined to play down those numbers).

Mystery solved.

UPDATE:  Eugene Volokh gets into this too, with a better explanation.