Question

two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 90 training rid
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 a greater median distance?

(b) which athlete went on the shortest training ride?

(c) which athlete had a smaller range of distances?

(d) which athlete had distances with a larger interquartile range (iqr)?

Explanation:

Step1: Recall box - plot properties

In a box - plot, the line inside the box represents the median. The left - most point (excluding outliers) represents the minimum value. The range is calculated as \( \text{Range}=\text{Max}-\text{Min} \). The inter - quartile range (IQR) is calculated as \( \text{IQR}=Q_3 - Q_1 \), where \( Q_1 \) is the first quartile and \( Q_3 \) is the third quartile.

Step2: Compare medians

For Athlete A, the median (the line inside the box) is at a higher value on the number line compared to Athlete B.

Step3: Compare minimum values

The left - most point (minimum value) for Athlete A is at a higher value than that of Athlete B. So, Athlete B has the shorter training ride.

Step4: Compare ranges

For Athlete A: Let's assume (from the box - plot) \( \text{Max}_A\approx40 \), \( \text{Min}_A\approx14 \), \( \text{Range}_A = 40 - 14=26 \). For Athlete B: \( \text{Max}_B\approx33 \), \( \text{Min}_B\approx8 \), \( \text{Range}_B=33 - 8 = 25 \). Wait, no! Wait, looking at the box - plot:
The range of Athlete A: The distance from the left - most non - outlier (or minimum) to the right - most non - outlier (or maximum) for Athlete A is smaller. The left - most point (excluding outliers) for Athlete A is higher than that of Athlete B, and the right - most point (excluding outliers) for Athlete A is lower than that of Athlete B. So, \( \text{Range}_A<\text{Range}_B \)

Step5: Compare IQR

The length of the box (which represents \( \text{IQR}=Q_3 - Q_1 \)) for Athlete B is longer than that for Athlete A.

Answer:

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