Question

two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 65 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 a smaller range of distances? (b) which athlete went on the shortest training ride? (c) which athlete had a greater median distance? (d) which athlete had distances with a larger interquartile range (iqr)?

Explanation:

Step1: Understanding Range

The range is calculated as \( \text{Range}=\text{Maximum}-\text{Minimum} \). Looking at the box - and - whisker plots, for Athlete A, the maximum and minimum are closer together compared to Athlete B.

Step2: Identifying the Shortest Ride

The left - most point of the whisker represents the minimum value. Athlete B's left - most whisker is at a smaller value on the distance scale than Athlete A's.

Step3: Comparing Medians

The line inside the box represents the median. Athlete B's median line is at a larger value on the distance scale than Athlete A's.

Step4: Understanding Inter - Quartile Range (IQR)

The IQR is \( \text{IQR}=Q_{3}-Q_{1} \) (where \( Q_{1} \) is the first quartile and \( Q_{3} \) is the third quartile). The length of the box in the box - and - whisker plot represents the IQR. Athlete B's box (IQR) is longer than Athlete A's.

Answer:

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