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 (in seconds) to run the first 5 km and the time (in seconds) to run between the 35 km and 40 km points, and then subtracting the 5-km time from the 35-40-km time. A positive value of this difference corresponds to a runner slowing down toward the end of the race. The histogram below is based on times of runners who participated in several different Japanese marathons ("Factors Affecting Runners' Marathon Performance," Chance [Fall 1993]: 24-30).
a. What are some interesting features of this histogram?
b. What is a typical difference value?
c. Roughly what proportion of the runners ran the late distance more quickly than the early distance?
