The Boston marathon is a very competitive race. To qualify for the Boston marathon, male runners must have completed a marathon in less than 3 hours and 5 minutes within the last year. Other marathons, such as the Chicago marathon, have no qualifying times. Anyone is able to run this race, even without completing a different marathon earlier in the year. Consider the groups of runners of each race: Boston marathon runners and Chicago marathon runners. Which group's finishing times for the marathon would most likely have the larger standard deviation?

Question

Nathan Hinton

Mathematics

11 September, 02:32

The Boston marathon is a very competitive race. To qualify for the Boston marathon, male runners must have completed a marathon in less than 3 hours and 5 minutes within the last year. Other marathons, such as the Chicago marathon, have no qualifying times. Anyone is able to run this race, even without completing a different marathon earlier in the year. Consider the groups of runners of each race: Boston marathon runners and Chicago marathon runners. Which group's finishing times for the marathon would most likely have the larger standard deviation?

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Answers (1)

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Nicholas Hammond · Answer 1

Chicago marathon runners

Step-by-step explanation:

Due to the strict qualifying time, the runners of the Boston marathon are going to very prepared, and quite close in their times. Since they are going to be close, the standard deviation is expected to be small.

Otherwise, in the Chicago marathon, anyone can run. This means that along with the professional runners, who are going to be very prepared, other unprepared runners will compete, and they are going to take a long time to complete the race, adding variation to the finishing times. The standard deviation is the square root of the variance, so since the variance for the Chicago marathon will be higher, the standard deviation also will