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Solved: How does the speed of a runner vary over the
Chapter 1, Problem 22E(choose chapter or problem)
Problem 22E
How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The accompanying histogram is based on times of runners who participated in several different Japanese marathons (“Factors Affecting Runners’ Marathon Performance,” Chance, Fall, 1993: 24–30).
What are some interesting features of this histogram? What is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distance?
Questions & Answers
QUESTION:
Problem 22E
How does the speed of a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to run the first 5 km and the time to run between the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The accompanying histogram is based on times of runners who participated in several different Japanese marathons (“Factors Affecting Runners’ Marathon Performance,” Chance, Fall, 1993: 24–30).
What are some interesting features of this histogram? What is a typical difference value? Roughly what proportion of the runners ran the late distance more quickly than the early distance?
ANSWER:
Solution:
Step 1 of 2:
Here, a histogram constructed based on the times of marathon runners is given.
The time is calculated for the first five kilometers and the time to cover 35-40 km distance are noted.
The difference between the two observed times of each runner is subtracted.The positive value indicates that the runner slows down as he reaches the end of the race and the negative value of the difference indicated that the runner runs fast at the end of the race.
Based on the histogram we need to find the required values.
