Question

(a) which athlete had a greater median distance? (b) which athlete had distances with a larger interquartile range (iqr)? (c) which athlete went on more rides longer than 15 miles? (d) which athlete went on the shortest training ride?

Explanation:

Step1: Find the median

The median is the middle value of the box - and - whisker plot. For Athlete B, the median is \(20\) miles. For Athlete A, the median is \(20\) miles. So, neither has a greater median.

Step2: Calculate the IQR

The IQR is \(Q3 - Q1\). For Athlete B: \(Q3 = 20\), \(Q1 = 15\), \(IQR=20 - 15=5\). For Athlete A: \(Q3 = 25\), \(Q1 = 15\), \(IQR = 25-15 = 10\). So, Athlete A has a larger IQR.

Step3: Count rides longer than 15 miles

For Athlete B: The number of rides longer than \(15\) miles is more (by counting the data points).

Step4: Find the shortest ride

The shortest ride is the minimum value. Athlete B's minimum is \(10\) miles, Athlete A's minimum is \(27\) miles. So, Athlete B had the shortest ride.

Answer:

(a) Neither; (b) Athlete A; (c) Athlete B; (d) Athlete B