Question

statistics using box - and - whisker plots to compare data sets. two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 65 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 went on the shortest training ride? (b) which athlete had distances with a larger interquartile range (iqr)? (c) which athlete had a greater median distance? (d) which athlete had a smaller range of distances?

Explanation:

Step1: Identify minimum value

The left - most end of the whisker represents the minimum value. For Athlete A, the minimum is around 10 miles and for Athlete B it is around 15 miles. So Athlete A went on the shortest training ride.

Step2: Calculate inter - quartile range (IQR)

IQR is the length of the box (Q3 - Q1). For Athlete A, Q1 is around 15 and Q3 is around 30, so IQR = 30 - 15=15. For Athlete B, Q1 is around 20 and Q3 is around 25, so IQR = 25 - 20 = 5. So Athlete A has a larger IQR.

Step3: Locate the median

The line inside the box represents the median. For Athlete A, the median is around 20. For Athlete B, the median is around 22.5. So Athlete B has a greater median distance.

Step4: Calculate the range

Range = Maximum - Minimum. For Athlete A, maximum is around 40 and minimum is around 10, so range = 40 - 10 = 30. For Athlete B, maximum is around 35 and minimum is around 15, so range = 35 - 15 = 20. So Athlete B has a smaller range of distances.

Answer:

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