22. How does the speed of a runner vary over the course of a marathon (a distanc

Question

22. 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?

Explanation / Answer

Answer:

The histogram is skewed to right. There may be few outliers around 700 seconds, still it is arguable. For a typical value: mode is between the 50-100 range, mean is greater around 200 - 250. The median would be in between. There appears to be only about 10 runners with negative values. It is difficult to tell, but the sample size, n is above 500 and maybe 1000 on the outside. Hence, the proportion of runners ran late distance very quickly than the early distance is around 1 to 2%. (10/1000 to 10/500)

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