![]() ![]() The Problem with Samples and EstimatorsĮssentially, the German Tank Problem demonstrates how to estimate the size of an entire population given only a limited sample. Today, the German Tank Problem is used by many AP® Stats teachers to demonstrate how to estimate a population parameter. The German Tank Problem has remained one of the most famous examples of applied mathematics in the twentieth century. In fact, it was critical to the Allies’ plan for D-Day. It turned out that the statisticians’ information was more accurate than the spies’: according to German records recovered after the war, they had produced 255 tanks for the month in question.Īs you can probably imagine, this was tactically useful information. ![]() When statisticians calculated the population maximum, their estimate was a mere 256 tanks per month. Statistical analysis proved far more accurate than estimates based on conventional intelligence gathering, which tended to wildly overestimate the number of tanks produced each month.įor example, traditional intelligence gathering put production of tanks at an absurdly high 1,400 tanks per month. They applied the same principles to estimating number and importance of factories, as well as a number of other manufactured munitions. Using serial numbers from damaged or captured German tanks, the Allies were able to calculate the total number of tanks and other machinery in the German arsenal.Īllied mathematicians were only able to collect a limited sample of German tanks, but used that sample as an estimator of the population maximum of German tanks. ![]() In World War II, each manufactured German tank or piece of weaponry was printed with a serial number. The German Tank Problem will help you do just that. Estimating the total population size, or population maximum, can let you draw more accurate conclusions about the sample and how it represents or fails to represent the entire population. Often, it can be useful to know the size of the total population when you are working with a limited sample size from a population of unknown size. ![]() Statisticians use estimators when dealing with samples from a larger population. The German Tank Problem is a famous statistical problem that helped the Allied Forces during World War II, and can help you with your AP® Statistics review. ![]()
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