Again, I am dumber for having read the New York Times 

The New York Times attempts to answer the age-old question of why straight men tend to have more sex partners than straight women:

EVERYONE knows men are promiscuous by nature. It’s part of the genetic strategy that evolved to help men spread their genes far and wide. The strategy is different for a woman, who has to go through so much just to have a baby and then nurture it. She is genetically programmed to want just one man who will stick with her and help raise their children.

Surveys bear this out. 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.

Well, I have deep reservations about the assumption that sexual promiscuity is a genetically transmitted trait (and about the entire field of evolutionary psychology as a whole), but let's leave that there.

Obviously, the total number of unique sexual relations that have taken place between men and women should be the same as reported by either gender. We can also assume that the populations of men and women over the lifetime of this survey are roughly equal. Therefore, the mean number of partners should be equal.

Sure, for cultural reasons, men may be more inclined to overreport and women may be more inclined to underreport the number of sexual partners they have had, but at a 7-to-4 clip? The problem with this article is of course, that the means and medians of two sets of data need not be the same.

Consider the following sets of numbers:

A: 3,5,5,5,5,7,7,7,7,7,7,9,9,9,9,11
B: 3,3,3,3,4,4,4,4,4,5,5,5,8,12,16,29

Both have the same means, but the median of A is 7 and the median of B is 4. Although I wouldn't doubt the possibility that there is some systematic discrepancy in the veracity of the results reported by men and women, it's also quite possible that most women have relatively few partners, but also that there is a small population of women who have large numbers of partners. I don't know if this is what happened, as I don't have access to the original data, but it is possible.

On a related note, here's an item in the WSJ by Carl Bialik about income distributions in New York City, and about how condensing an entire data set into just one number (usually the mean or median) throws out a lot of information. It's really elementary stuff, and I think it's a borderline national crisis that so many people in America are so ignorant about basic statistics.

(HT: this guy)

EDIT: Jordan Ellenberg says his piece on Slate. He claims that the 12.7 and 6.5 figures quoted above are means, not medians (which would make sense, since 12.7 is not a possible median value for a set of integer-valued data). So there is definitely some miscounting going on. Since he mentions the phrase "Ted Turners of sex", I wonder if the researchers in the original sex surveys accidentally counted instances of bestiality. And now you, the reader, are dumber for having read this post to the end.


Amusing graphic to illustrate it.

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