The histogram and box plots below show the distribution of finishing times for m
ID: 3273479 • Letter: T
Question
The histogram and box plots below show the distribution of finishing times for male and female winners of the New York Marathon between 1970 and 1999. (a) What features of the distribution are apparent in the histogram and not the box plot? What features are apparent in the box plot but not in the histogram? (b) What may be the reason for the bimodal distribution? Explain. (c) Compare the distribution of marathon times for men and women based on the box plot shown below. (d) The time series plot shown below is another way to look at these data. Describe what is visible in this plot but not in the others.Explanation / Answer
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a.The feature of bimodality is visible in histogram , which a box plot can't tell
The feature apparent in box plot but not in histogram is that of outlier detection. Although outliers are visible in histogram, the histrogram can't say that these are outliers, whereas in boxplot that' clearly visible.
b. The 2 modes are of 2 genders. One for male and other for females.
c. Clearly, boxplot suggests the following:
1. Male take lesser time to complete marathon than females. i.e. 2.2 vs. 2.5 for females
2. The distribution of men is not as skewed as women'. women' is right skewed with very high outliers.
d. The time series gives out results ( marathon time by gender) w.r.t to time this time. This is what is missing from previous plots. It is good to know this because it may so happen that the graphs of men and women are not similar, and hence the Marathon time distribution is different
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