Question

using box-and-whisker plots to compare data sets
athlete b
distance (in miles)
5 10 15 20 25 30 35 40 45
(a) which athlete went on the shortest training ride?
select
(b) which athlete had a smaller range of distances?
select
(c) which athlete had a greater median distance?
select
(d) which athlete had distances with a larger interquartile range (iqr)?

Explanation:

Step1: Determine the shortest training ride

The left - most point (minimum value) of the box - and - whisker plot represents the shortest distance. For Athlete B, the minimum value is higher than that of Athlete A. So Athlete A has the shortest training ride.

Step2: Compare the ranges

The range is calculated as \(Range = Max - Min\). For Athlete A, assume \(Max_A\) and \(Min_A\), for Athlete B, assume \(Max_B\) and \(Min_B\). By observing the plots, \(Max_A - Min_A

Step3: Compare the medians

The median is the middle line of the box in the box - and - whisker plot. By observing, the median of Athlete B is higher than that of Athlete A.

Step4: Compare the inter - quartile ranges (IQR)

The IQR is \(Q3 - Q1\) (where \(Q1\) is the first quartile and \(Q3\) is the third quartile). By observing the length of the box (which represents the IQR), the box for Athlete B is longer. So Athlete B has a larger IQR.

Answer:

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