Question

two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 95 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 went on the shortest training ride?
(c) which athlete went on more rides longer than 24 miles?
(d) which athlete had a greater median distance?

Explanation:

Step1: Recall IQR concept

IQR = Q3 - Q1. For box - and - whisker plot, length of box represents IQR.

Step2: Compare box lengths

Athlete A's box length is smaller. Athlete B's box is longer. So Athlete B has larger IQR.

Step3: Identify shortest ride

The left - most point of the whisker represents the minimum value. Athlete A has left - most point at a lower value. So Athlete A went on the shortest training ride.

Step4: Analyze rides longer than 24 miles

For Athlete A, 24 miles is to the left of the median and box. For Athlete B, more of the data (right half of box and right whisker) is above 24 miles. So Athlete B went on more rides longer than 24 miles.

Step5: Compare medians

The line inside the box represents the median. Athlete B's median line is at a higher value on the number line. So Athlete B has a greater median distance.

Answer:

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