How does the speed of vary over the time to run to a runner slowing down toward

Question

How does the speed of vary over the time to run to a runner slowing down toward the end of the Japanese marathons.t a runner vary over the course of a marathon (a distance of 42.195 km)? Consider determining both the time to nun the first m the 35-km and 40-km points, and then subtracting the former time from the latter time. A positive value of thi Frequency race. The accompanying histogram is based on times of 1000 runners who participated in several diffeent a Iso 100 -100 100 200 300 00 500 600 700 00 Time difference positively skewed a small spread mostly positive values negatively skewed Roughly what proportion of the runners ran the late distance more quickly than the early distance? (Round your answer to two decimal places.)

Explanation / Answer

a)

A right-skewed distribution has a long right tail. Right-skewed distributions are also called positive-skew distributions. That’s because there is a long tail in the positive direction on the number line. The mean is also to the right of the peak.

positive-skew distribution

b) For a typical value: the mode is in the 50-100 range; the mean is somewhat larger (because it is skewed right), maybe around 200-250 (just a guess). The median would be in between. around 150 may be

c) There seem to be only about 10 runners with negative values for the distance. It's hard to tell, but the sample size n is clearly above 500, and maybe 1,000 on the outside. Thus, the proportion of runners ran the late distance more quickly than the early distance is around 1 to 2 % (10/1000 to 10/500).

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