How Many Taxis?

You are standing in the rain trying to hail a cab in a large city. While waiting, seven cabs pass by that already have a passenger. The numbers on the cabs are 405, 73, 280, 179, 440, 301, 218.

Suppose you want to estimate the number of taxis in the city while you are waiting. Assuming that the taxis are numbered consecutively from 1 to N and all are still in service, how can you use the observed numbers to estimate N, the total number of taxis in the city?

How many taxis do you think there are? How can you test your method for estimating N?