# Estimating the Size of a Population

Estimating the Size of a Population

Suppose that in a marathon each runner has a running number on their back but we do not know , the total number of runners. At some point along the course we observe random runners and write down their running numbers , . What would be our estimate of ? Let be largest of the observed numbers . It can be shown that a good estimate of is . The Demonstration shows examples of this estimate when is 100. It also shows the frequency distribution of the percent estimation error, when the is a random integer between 100 and 1000.

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