# Average statistic != average male's statistic

The Star Tribune had a page one teaser for an article about a newly released survey on drug use and (heterosexual) sexual behavior of U.S. adults. It stated that "The typical man has sex with seven women in his lifetime."

This phrasing really sets my teeth on edge. Who is this typical man? Does he also have a fractional number of children? Or is that the "average man"? Is the typical man married or unmarried? Has the typical man taken 26% of a dose of cocaine?

At least the statistic reported is a median, not a mean. You can download the survey results yourself. Males 20 through 59 have had a median of 6.8 female sexual partners in their lifetime. (Why is it a fraction value instead of either 6 or 7? I thought the median was the 50th percentile. It's reported as 6.8 with a standard error of 0.4, which I guess tells us that the true statistic might be either 6 or 7.)

The distribution they gave is:
16.7%: 0 or 1 partners
33.8%: 2 to 6 partners
20.7%: 7 to 14 partners
28.9%: 15 or more parners

You can say a lot of things with this data set. You can say that the most likely bucket into which any given male will fall is 2-6. I'm guessing the mode is either 1 or 2, probably 1. In any case, if you have to guess the statistic for a random male, the guess that's most often correct will be a number well below 7.

But you shouldn't say that the "typical man's" number of partners is seven. The number 7 is only interesting if you want your guess to be too high just as often as it's too low. Perhaps men who sleep with only seven women during their lifetime are atypical--- the distribution could be bimodal with peaks around 1-2 and 14-16. It is even possible that none of the survey-takers had had exactly seven partners!

Suppose 51% of American voters oppose the war in Iraq. Would it be sensible to say that the "typical voter" opposed the war? I don't think so. You just can't compress a distribution down to a single statistic and pretend that you've said something meaningful.

ETA: Bonus link! Jordan Ellenberg chastises the NYT for confusing "significant" and "statistically significant." 3 IQ points may be statistically signficant, but it's not all that meaningful.
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