Average is Over

There has been an increase in the mean body-mass index since the 19th century but even more strikingly there has been an increase in the variance, what we might call an increase in weight inequality. More here.

Hat tip: Andrew Leigh.


I don't see why this supports Average is Over; a Normal distribution is with a higher mean and variance is still a Normal distribution.

To say that the historical variance was ''right'' and that the new variance is ''wrong'' is an opinion, not a statement supported by evidence.

I see no Gaussians. All those distributions look like they skew to the right, especially the modern, non-prisoner one.

That doesn't make one of those distributions "right" or "wrong" - it just means that in one of those distributions, being far from average is more common. Which is what Alex said.

Regardless of whether it's truly gaussian or not, the real question is not whether variance has increased but whether mean/variance has increased. If the ratio is the same, then the fact that the variance increased is boring.

Just eyeballing the graph the mean seems to have increased by ~ 10% (23 -> 26 ?) while the variance seems to have changed by almost 100% (roughly guesstimating from the FWHM). Definitely a much wider spread now. Which does make the average a much less useful marker since the fraction of the population that is somewhat described by the average has fallen and there is no longer a useful "typical" BMI.

Weight could never really be distributed normally since it is truncated at zero, more precisely truncated at the lowest possible weight at which a creature born of humans could reach adulthood and be considered human. Furthermore it is not truncated upward. So obviously it will be skewed. That being said, it looks pretty darn gaussian to me.

If it is true that the 19th century sample is from prison, there are many reasons for it to be homogenous. One is the relatively narrower age range (unless they controlled for that). Another is that criminals may be selected for physical characteristics - I believe there was an MR post on this. I recall that the punch line was that in the 19th century scrawny people had a harder time making an honest living and so proportionally more of them turned to crime. There could also be correlations in getting caught and in convincing a jury you are guilty.

People live a good deal longer now than in the C19. That should give pause to those who believe that correlation implies cause.

But do people who reach adulthood actual live a good deal longer? I don't think so

I'm sure it hass nothing to do with the 19th century data being from prisoners, and the 20th century from a nationwide survey.

But if all you have is a hammer...

Next you'll be asserting that it doesn't matter if some people get richer, while others only get less richer, but that's its the individual results that matter, not how much "inequality" there is overall.

The statistical margin-of-error is huge... in this purported "measure" of a 'population' over 2 centuries.
And the methodology is mysterious.

Mere speculation, not measurement.

It's a bounded distribution -- there's only so low a BMI can go, and there's no particular reason to expect the low end to increase as the average increases. In a case like this, when the mean increases there's a natural increase in the variance. In short, it's an expected result.

But it does support the argument that the average is less relevant. Instead of clothes coming Small, Medium, Large we now commonly have XS (in part because S is now bigger than an S used to be), XL and XXL (and beyond).

Perhaps the fattest 1% should have forced liposuction, and that fatty tissue redistributed to the leanest Americans!

Taft was the last really fat President. Back then, being a fat cat was a mark of wealth, because food was expensive.

BMI is a linear division of weight by height.

Since weight (of a geometric object) increases with the cube of the height, wouldn't we normally expect the mean to shift higher simply as an effect of people getting taller, even holding %body fat constant?

of course the variance issue is more interesting than the mean shift, but doesn't that just follow the greater choice in consumption, occupation, and leisure options available today? (a result of increased prosperity)

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