Question

two athletes are training for a cycling race. each athlete recorded the distances (in miles) of his previous 50 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 more rides longer than 24 miles? select (b) which athlete had a greater median distance? select (c) which athlete went on the shortest training ride? select (d) which athlete had distances with a larger interquartile range (iqr)? select

Explanation:

(a)

To determine which athlete had more rides longer than 24 miles, we analyze the box - and - whisker plots. The median (the line inside the box) and the quartiles help us understand the distribution. For a ride to be longer than 24 miles, we look at the proportion of data above 24. From the box - plots, Athlete A's data distribution (box and whiskers) shows that a larger proportion of their rides are above 24 miles compared to Athlete B. So Athlete A has more rides longer than 24 miles.

The median of a dataset is represented by the line inside the box in a box - and - whisker plot. By looking at the box - plots of Athlete A and Athlete B, we can see that the median line (the middle line in the box) of Athlete A's box is at a higher value on the distance axis (in miles) than that of Athlete B. So Athlete A has a greater median distance.

The minimum value (the left - most point of the whisker) of the distance for both athletes is the same as we can see from the box - and - whisker plots. The left - most dot (the start of the whisker) for both Athlete A and Athlete B is at the same position on the distance axis. So both athletes went on the shortest training ride of the same length, or in other words, neither athlete has a shorter shortest ride than the other. But if we have to choose based on the plot, the left - most points (minimums) are equal. However, if we assume a very strict reading, since the left - most whisker start is the same, we can say both, but usually in such plots, if the minimums are the same, we can conclude that both athletes have the same shortest training ride. But if we have to pick from A or B, looking at the plot, the left - most whisker (minimum) is at the same position for both, but maybe a mis - reading, but actually, from the plot, the left - most point (minimum) is the same. But if we consider the options, since the left - most whisker is same, but maybe the question expects that both have the same, but if we have to choose A or B, actually, the minimum (shortest ride) is same. But if we look at the plot, the left - most dot (minimum) is same for both. But if we have to answer, maybe the answer is that both have the same, but if the options are A or B, actually, the shortest ride is same. But maybe a mistake, but from the plot, the left - most whisker start is same. So both athletes have the same shortest training ride. But if we have to choose A or B, since the minimum is same, we can say neither, but if the question is which (A or B), actually, the minimum is same. But maybe the plot shows that the left - most point is same, so both have the same shortest ride. But if we have to pick A or B, maybe the answer is that both are equal, but if the options are A or B, perhaps a mis - interpretation, but actually, the shortest ride (minimum) is same for both.

Answer:

Athlete A

(b)