Question

two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 80 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 had a greater median distance? (c) which athlete went on the shortest training ride? (d) which athlete had a smaller range of distances?

Explanation:

Step1: Recall box - and - whisker plot properties

The inter - quartile range (IQR) is the length of the box (Q3 - Q1), the median is the line inside the box, the end of the left - most whisker is the minimum value, and the range is the difference between the maximum and minimum values.

Step2: Calculate IQR for Athlete A

For Athlete A, assume Q1 is around 20 and Q3 is around 30. So, IQR(A)=$30 - 20=10$.

Step3: Calculate IQR for Athlete B

For Athlete B, assume Q1 is around 25 and Q3 is around 35. So, IQR(B)=$35 - 25 = 10$. But visually, if we consider more precisely, the box for Athlete B is slightly longer, so Athlete B has a larger IQR.

Step4: Find the median for each athlete

The median for Athlete A is around 25. The median for Athlete B is around 30. So, Athlete B has a greater median.

Step5: Determine the minimum value

The left - most point (start of the whisker) for Athlete A is around 15 and for Athlete B is around 15. But if we look closely, Athlete A's left - most point is at a lower value, so Athlete A went on the shortest training ride.

Step6: Calculate the range for each athlete

For Athlete A, assume the maximum is around 40 and the minimum is around 15, so range(A)=$40 - 15=25$. For Athlete B, assume the maximum is around 45 and the minimum is around 15, so range(B)=$45 - 15 = 30$. So, Athlete A has a smaller range.

Answer:

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