Question

use the box-and-whisker plots to answer the questions. (a) which athlete had a greater median distance? select (b) which athlete had distances with a larger interquartile range (iqr)? select (c) which athlete had a smaller range of distances? select (d) which athlete went on the shortest training ride? select

Explanation:

(a)

Step1: Recall median in box - plot

In a box - plot, the line inside the box represents the median.

Step2: Compare medians of Athlete A and B

For Athlete A, the median (the line inside the box) is around 24 - 26 (let's say 25 for approximation). For Athlete B, the median (the line inside the box) is around 29 - 31 (let's say 30 for approximation). Since 30>25, Athlete B has a greater median distance.

Step1: Recall IQR in box - plot

The inter - quartile range (IQR) is calculated as \(IQR = Q_3 - Q_1\), where \(Q_3\) is the third quartile (the right end of the box) and \(Q_1\) is the first quartile (the left end of the box).

Step2: Calculate IQR for Athlete A and B

For Athlete A: Let \(Q_1\) be around 19 - 21 and \(Q_3\) be around 29 - 31. \(IQR_A=Q_3 - Q_1\approx30 - 20 = 10\). For Athlete B: Let \(Q_1\) be around 17 - 19 and \(Q_3\) be around 32 - 34. \(IQR_B=Q_3 - Q_1\approx33 - 18 = 15\). Since \(15>10\), Athlete B has a larger IQR.

Step1: Recall range in box - plot

The range is calculated as \(Range = Maximum - Minimum\).

Step2: Calculate range for Athlete A and B

For Athlete A: Let \(Maximum\) be around 33 - 35 and \(Minimum\) be around 9 - 11. \(Range_A=Maximum - Minimum\approx34 - 10 = 24\). For Athlete B: Let \(Maximum\) be around 34 - 36 and \(Minimum\) be around 12 - 14. \(Range_B=Maximum - Minimum\approx35 - 13 = 22\). Since \(22<24\), Athlete A has a smaller range.

Answer:

Athlete B

(b)