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Chapter 1: Q22E (page 27)

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 (鈥淔actors Affecting Runners鈥� Marathon Performance,鈥� Chance, Fall, 1993: 24鈥�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?

Short Answer

Expert verified

There are outliers present, they are, 650, 700 and 750. The distribution is positively skewed.

The proportion of the runners ran the late distance more quickly than the early distance is 0.001.

Step by step solution

01

Given information

A histogram is provided based on times of runners who participated in several different Japanese marathons.

02

 Step 2: State the features

The features of the provided histogram are as follows,

1)The distribution is positively skewed.

2)The outliersarefrom 650 to 750.

3)The typical or representative difference value is 350.

4)The histogram is unimodal with the mode of 100 seconds approximately.

03

Compute the proportion

The size of the sample is,

\(90 + 190 + 180 + 160 + 120 + 80 + 60 + 40 + 30 + 20 = 970\)

The proportion of the runners ran the late distance more quickly than the early distance is computed as,

\(\begin{array}{c}\frac{{negative\;time\;difference}}{{Total\;sample\;size}} &=& \frac{{10}}{{970}}\\ &=& 0.001\end{array}\)

Therefore, theproportion of the runners ran the late distance more quickly than the early distance is 0.001.

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