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 (€œFactors Affecting Runners€™ Marathon Per formance,€ 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?

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Frequency 200 150 100 50 Time 100 0 100 200 300 400 500 600 700 800 derence