Question

data analysis and probability
using box-and-whisker plots to compare data sets
athlete a
athlete b
5 10 15 20 25 30 35 40 45
distance (in miles)
(a) which athlete went on the shortest training ride?
athlete a
(b) which athlete went on more rides longer than 23 miles?
athlete b
(c) which athlete had distances with a larger interquartile range (iqr)?
both had the same iqr
(d) which athlete had a greater median distance?
athlete b

Explanation:

Step1: Analyze part (a)

The shortest training ride is the minimum value in the box - and - whisker plot. Looking at the plots, Athlete A's minimum (the leftmost dot) is to the left of Athlete B's minimum, meaning Athlete A has the shortest training ride.

Step2: Analyze part (b)

To find which athlete has more rides longer than 23 miles, we look at the box - and - whisker plots. The median (middle line in the box) and the quartiles: Athlete B's data is more spread out above 23 miles. Also, visually, the number of data points (implied by the box - plot) for rides longer than 23 miles is more for Athlete B.

Step3: Analyze part (c)

The inter - quartile range (IQR) is the difference between the third quartile (\(Q_3\)) and the first quartile (\(Q_1\)) (\(IQR = Q_3 - Q_1\)). By looking at the box - and - whisker plots, the length of the box (which represents \(IQR\)) for both athletes is the same. So both have the same IQR.

Step4: Analyze part (d)

The median is the middle line in the box of the box - and - whisker plot. Looking at the plots, Athlete B's median (middle line) is at a higher value (more miles) than Athlete A's median. So Athlete B has a greater median distance.

Answer:

(a) Athlete A
(b) Athlete B
(c) both had the same IQR
(d) Athlete B