OT: Nerdy fat stats

Arthur Smith (a British comedian) is fond of telling the following joke
about an unprotected national stereotype:

One in three Americans weighs as much as the other two.

Concise and clever. The best sort of joke.

But how clever is it? There are a lot mathematicians of various sorts
here. Perhaps you can help. What sort of weight distribution could
produce a result like that? Would it have to be extraordinarily skewed
to one side or extraordinarily platykurtic or leptokurtic and would such
a distribution be representative of a population that was very fat or
very thin or entirely unexceptional when compared with the rest of the
world?

My eyeballed guess is that, if you include all ages and take 'weight of
one in three' to mean 'the mean of the heaviest third', an entirely
normal normal distribution would do it and that this wouldn't say
anything about obesity.

Comments?

--
VB
.

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