Question

two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 80 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 went on more rides longer than 35 miles?
(d) which athlete went on the shortest training ride?

Explanation:

Step1: Recall the properties of box - and - whisker plots

The inter - quartile range (IQR) is the length of the box in a box - and - whisker plot. The median is the line inside the box. The number of data points above a certain value can be compared by looking at the whiskers and the box. The minimum value is the left - most point (excluding outliers if any).

Step2: Compare the IQR

For Athlete A, the box (IQR) is relatively long. For Athlete B, the box (IQR) is relatively short. So, Athlete A has a larger IQR.

Step3: Compare the medians

The median of Athlete B (the line inside Athlete B's box) is to the right of the median of Athlete A (the line inside Athlete A's box). So, Athlete B has a greater median.

Step4: Compare the number of rides longer than 35 miles

For Athlete A, the whisker and part of the box to the right of 35 miles is relatively short. For Athlete B, the whisker and part of the box to the right of 35 miles is relatively long. So, Athlete B has more rides longer than 35 miles.

Step5: Compare the shortest rides

The left - most point (minimum value) of Athlete A is to the left of the left - most point (minimum value) of Athlete B. So, Athlete A went on the shortest training ride.

Answer:

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