Questions: Two athletes are training for a cycling race. Each athlete recorded the distance (in miles) of their previous 75 training rides. The box-and-whisker plots below (sometimes called boxplots) summarize the distances recorded for each athlete. Use the box-and-whisker plots to answer the questions. (a) Which athlete had distances with a larger interquartile range (IQR)? (b) Which athlete had a greater median distance? (c) Which athlete had a smaller range of distances? (d) Which athlete went on the shortest training ride?

Two athletes are training for a cycling race. Each athlete recorded the distance (in miles) of their previous 75 training rides. The box-and-whisker plots below (sometimes called boxplots) summarize the distances recorded for each athlete. Use the box-and-whisker plots to answer the questions. (a) Which athlete had distances with a larger interquartile range (IQR)? (b) Which athlete had a greater median distance? (c) Which athlete had a smaller range of distances? (d) Which athlete went on the shortest training ride?
Transcript text: Two athletes are training for a cycling race. Each athlete recorded the distance (in miles) of their previous 75 training rides. The box-and-whisker plots below (sometimes called boxplots) summarize the distances recorded for each athlete. Use the box-and-whisker plots to answer the questions. (a) Which athlete had distances with a larger interquartile range (IQR)? (b) Which athlete had a greater median distance? (c) Which athlete had a smaller range of distances? (d) Which athlete went on the shortest training ride?
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Solution

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Solution Steps

Step 1: Interquartile Range (IQR)

The IQR is the difference between the first quartile (Q1) and the third quartile (Q3). Visually, this is the length of the box. Athlete B's box is longer, thus Athlete B has a larger IQR.

Step 2: Median Distance

The median is represented by the vertical line inside the box. Athlete A's median is higher than Athlete B's.

Step 3: Range of Distances

The range is the difference between the minimum and maximum values. Visually, it's the distance between the ends of the whiskers. Athlete A's range is smaller (13 to 27 miles) than Athlete B's (8 to 30 miles).

Final Answer

(a) Athlete B (b) Athlete A (c) Athlete A

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