56 58 60 62 64 66 68 70 72 74 76 78 Height (inches) 3.66 Marathon Times The hist

Question

56 58 60 62 64 66 68 70 72 74 76 78 Height (inches) 3.66 Marathon Times The histogram of marathon times includes data for men and women and also for both an Olympic marathon and an amateur marathon. Greater values indicate slower runners. (Sources: www.forestcityroadraces.com and www.runnersworld.com) 90 80 7 60 g 50 40 30 F 20 10 8000 120001600020000 Times for Two Marathons (seconds) a. Describe the shape of the distribution. b. What are two different possible reasons for the two modes? c. Knowing that there are usually fewer women who run marathons than men and that more people ran in the amateur marathon than the Olympic marathon, look at the size of the mounds and try to decide which of the reasons stated in part b is likely to cause this. Explain. 3.67 Law School GPAs The histogram shows the minimum GPA of accepted students at 181 nationally ranked law schools in 2006. (Source: www.ilrg.com) a. State an approximate value for the mean GPA b. Here is a proposed method for finding an approximation to the

Explanation / Answer

(a)

The histogram shows that right tail is greater than left tail. That is distribution is skewed to right. It is not symmetric.

Histogram shows two peaks so it is bimodal.

(b)

First reason:

Histogram shows the marathon times for both men and women. So it is possible that one peak shows the mode for distribution of marathon times for women and second  peak shows the mode for distribution of marathon times for men.

Second reason:

Histogram shows the marathon times for both Olympic marathon and amateur marathon. So it is possible that one peak shows the mode for distribution of marathon times for Olympic marathon and second  peak shows the mode for distribution of marathon times for amateur marathon.

(c)

It is likely that number of women who rum marathon is signficantly low so it seems that first reason of part b caused bimodal distribution.

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