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 : Step 1 of 1 : A very large percentage of data values are greater than 0, which indicates that most runners do slow down at the end of the race. The histogram is positively skewed, which means some runners slow down compared to others. A typical value for this data would be in the neighbourhood of 200 seconds. The proportion of the runners who ran the last 5km faster than they did the first 5km is very small, about 1 to 2%.