There are currently 174 books on my Amazon wishlist that I could order directly from Amazon. (My wishlist has a total of 195 books, but 21 are only available from other sellers.) Total price is approximately $3,549 (I rounded all prices to whole dollars), for a mean of approximately $20 per book.

But the median price of a book on my wishlist is (again to the nearest whole dollar) $16; the difference between the median and the mean is a hint that the distribution is skewed. And there are actually two peaks — one centered on $10 and one centered on $16-17. The distribution looks like this:

I’ve cut off the histogram at $100, which omits Mitchell’s *Machine Learning* at a list price of $168.16. Here’s a zoomed-in version omitting the 23 most expensive (all those over $30):

The two peaks are easy to explain: paperbacks and hardcovers, respectively. The long right tail is pretty much exclusively made up of technical books. I’d suspect that for those who read a lot but don’t buy technical books, the bimodality holds up but there’s a lot less skewness.

(If you look closely you might see a third peak, at around $60, but in a data set of this size I’m not sure that’s real.)

This is a much less depressing example than my standard example of a bimodal distribution, salaries of first-year lawyers.

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The existence of price points certainly validates the choice of a multi-modal distribution. But it looks more like a multi-modal modulated by an exponential decay that depends on ones perception of a cost / benefit relationship which can further be affected by other phenomena as well (See for example the framing effect).

Reblogged this on Stats in the Wild and commented:

I’d like to see density estimates added to the histograms, but this is interesting.

[…] example of a real-world bimodal distribution! Maybe you have a ready example if you teach stat, but here’s a really nice example from Michael Lugo: Book prices. Before you read his post, you should make a guess as to why the […]

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[…] around different price points, depending on whether your looking at paperbacks or hardcovers as God Plays Dice explains. If the gap between paperback and hardcovers isn’t wide enough for you, imagine you could […]