By Ben Blatt

In 1964, Mosteller and Wallace published Inference and Disputed Authorship: The Federalist. The paper used statistical analysis to try to determine if James Madison, Alexander Hamilton, or John Jay was the author of the unaccredited essays that were part of The Federalist Papers. They approached this historical mystery by using differences in word frequencies and Bayesian statistics. While controversial, similar methods have been used to investigate other authorship debates such as Shakespeare’s sonnets and plays. The same can be done for sports articles. While it would certainly be easier to look at the author’s name right underneath the title than to perform a statistical analysis of authors, I thought it would be fun anyways.

Math teachers have been using the “German Tank Problem” for awhile to teach estimators. It goes something like this.

The Allies capture five German tanks. Suppose that the serial numbers on the tanks are 15, 23, 59, 83, and 109. Provide an estimate of the number of tanks that were produced.

You can see that your estimate would be a great deal lower than the estimate if the serial numbers were 1015, 2394, and 9438.

The story and accompaning math problem was written about in the Guardian. My favorite line, which turned out to be true, was this:

The statisticians believed that the Germans, being Germans, had logically numbered their tanks in the order in which they were produced.

It turns out that the statisticians were spot on:

By using this formula, statisticians reportedly estimated that the Germans produced 246 tanks per month between June 1940 and September 1942…

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…