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Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. In January 2009, 22 men and 31 women entered the 19–24 age class. Finish times in minutes are as follows ( Naples Daily News, January 19, 2009). Times are shown in order of finish. a. George Towett of Marietta, Georgia, finished in first place for the men and Lauren Wald of Gainesville, Florida, finished in first place for the women. Compare the first-place finish times for men and women. If the 53 men and women runners had competed as one group, in what place would Lauren have finished? b. What is the median time for men and women runners? Compare men and women runners based on their median times. c. Provide a five-number summary for both the men and the women. d. Are there outliers in either group? e. Show the box plots for the two groups. Did men or women have the most variation in finish times? Explain.
STATISTICS F/BUSINESS+ECONOMICS-TE...
STATISTICS F/BUSINESS+ECONOMICS-TE...
Naples, Florida, hosts a half-marathon (13.1-mile race) in January each year. The event attracts top runners from throughout the United States as well as from around the world. In January 2009, 22 men and 31 women entered the 19–24 age class. Finish times in minutes are as follows (Naples Daily News, January 19, 2009). Times are shown in order of finish.
- a. George Towett of Marietta, Georgia, finished in first place for the men and Lauren Wald of Gainesville, Florida, finished in first place for the women. Compare the first-place finish times for men and women. If the 53 men and women runners had competed as one group, in what place would Lauren have finished?
- b. What is the median time for men and women runners? Compare men and women runners based on their median times.
- c. Provide a five-number summary for both the men and the women.
- d. Are there outliers in either group?
- e. Show the box plots for the two groups. Did men or women have the most variation in finish times? Explain.
a.
Compare the first place finish times for men and women and to find the place where Lauren have finished, if the 53 men and women runners had completed as one group.
Explanation of Solution
Calculation:
The given information is that the data represent the finish times (in minutes) for both men and women. There are 22 men and 31 women who entered the 19–24 age class.
The first place runner in the men’s group finished in 65.30 minutes, and the first place runner in the women’s group finished in 109.03 minutes.
By taking the difference between them, the following is obtained:
b.
Find the median time for men and women runners and to compare men and women runners based on their median times.
c.
Find the five-number summary for both men and women.
d.
Check whether there are any outliers in either group.
e.
Draw the boxplots for the two groups. Explain whether men or women have the most variation in finish times.
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