How does the speed of a runner vary over the course of a marathon (a distance of

Question

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 1000 runners who participated in several different Japanese marathons.†

What are some interesting features of this histogram? (Select all that apply.)

symmetric

negatively skewed

positively skewedsmall

sample size

small spread

mostly positive values

Approximately what is the median difference value? (Enter an approximate value.)
sec

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

Solution:

a) positively skewed

mostly positive values

Explanation:

The histogram is clearly skewed right it is strong.

b) There may be a few outliers around 700 seconds. the mode is in the 50-100 range; the mean is larger (because it is skewed right), maybe around 200-250 . The median would be in between.

c) There seem to be only about 10 runners with negative values for the distance. 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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