### German Tank Problem

In WW2, the Allies estimated German average monthly tank production using statistical analysis of their serial numbers. They were off by just one.

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The German Tank Problem is a way to estimate the total population size from a small sample. It's commonly used in AP statistics to teach about estimators. The problem was originally developed by the Allies during World War II, when it was used to estimate the total number of German tanks from a small number of serial numbers from captured, destroyed, or observed tanks. It was extended to estimate the number of factories and other manufactured parts. Today, the formula has been applied for wide-reaching applications like estimating the number of iPhones sold.

In World War II, the Allies did not know how many tanks the Germans were making. After a set of German Mark V tanks were captured and statisticians theorized (correctly) that the Germans numbered those tanks sequentially as they came off the production line. The statisticians estimated that 246 tanks were being made per month between June 1940 and September 1942; This was a significant reduction from intelligence estimates which put the number at about 1400. After the war, the Allies inspected the German's production records and found that the true number of tanks produced per month was 245 — extremely close to the statisticians' estimate.

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