How does the speed of a runner vary over the course of marathon (a distance of 4

Question

How does the speed of a runner vary over the course of marathon (a distance of 42.195 km)? Consider determining both the time to run the first the time to run between the 35-km and 40-km points, and then subtracting the former 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 several different Japanese marathons. What are some interesting features of this histogram? (Select all that apply.) symmetric negatively skewed small sample size mostly positive values positively skewed small spread

Explanation / Answer

Feaures:

Correct options:

- mostly positive values

- positively skewed.

REASON:

1. The histogram is not symmetric. - Note that the left side of the mid value is not the same as the right side of mid value.

2. Negatively skewed is wrong.

Skewness = (mean - mode)/SD.

Here, mean > mode.

So, skewness is positive.

3. small sample size - wrong, as we can see frequencies over 150.

4. mostly positive values - correct. Note that only negativa values are shown in the histogram: first rectangle from the left, which is very small.

5. positively skewed: Correct, as explained in2 above.

6. small spread - wrong, as we can see that the histogram is sufficiently spread about the middle value.

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