two athletes are training for a cycling race. each athlete recorded the distance (in miles) of their…

two athletes are training for a cycling race. each athlete recorded the distance (in miles) of their previous 70 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)? choose one (b) which athlete had a greater median distance? choose one (c) which athlete went on more rides longer than 35 miles? choose one (d) which athlete went on the shortest training ride? choose one

two athletes are training for a cycling race. each athlete recorded the distance (in miles) of their previous 70 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)? choose one (b) which athlete had a greater median distance? choose one (c) which athlete went on more rides longer than 35 miles? choose one (d) which athlete went on the shortest training ride? choose one

Answer

Explanation:

Step1: Recall box - and - whisker plot properties

The IQR is the length of the box (Q3 - Q1), the line inside the box is the median, and the whiskers show the range of data. Points beyond the whiskers are outliers.

Step2: Calculate IQR for each athlete

For Athlete A: Q1 is around 25 and Q3 is around 35, so IQR(A)=$35 - 25=10$. For Athlete B: Q1 is around 20 and Q3 is around 30, so IQR(B)=$30 - 20 = 10$. But visually, the box for Athlete A is slightly wider.

Step3: Identify the median

The median for Athlete A is around 30. The median for Athlete B is around 27.5. So Athlete A has a greater median.

Step4: Check number of rides longer than 35 miles

For Athlete A, the right - whisker ends around 35, so no rides longer than 35 miles (excluding outliers). For Athlete B, the right - whisker extends beyond 35, so Athlete B has more rides longer than 35 miles.

Step5: Determine the shortest ride

The left - whisker of Athlete B starts at a lower value (around 15) compared to Athlete A (around 20). So Athlete B went on the shortest training ride.

Answer:

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