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.
9 thoughts on “A real-life example of a bimodal (or trimodal?) distribution”
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.
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