Stats in the Wild

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…