Let's analyze each part of the question based on the box-and-whisker plots for Athlete A and Athlete B.

Observations from the Box-and-Whisker Plots

1. Rides longer than 15 miles: This refers to the portion of the box plot for distances greater than 15 miles.
2. Interquartile Range (IQR): The IQR is the length of the box, showing the range from the first quartile (Q1) to the third quartile (Q3).
3. Shortest Training Ride: This would be represented by the smallest data point (leftmost end of the whisker).
4. Median Distance: The median is the line inside the box, which shows the middle value of the data set.

Answers Based on Observations

1. (a) Which athlete went on more rides longer than 15 miles?

   • Look at the starting point of each box plot. Athlete A’s rides are generally longer, so Athlete A likely went on more rides longer than 15 miles.

2. (b) Which athlete had distances with a larger interquartile range (IQR)?

   • The IQR is the length of the box. Athlete A’s box is wider, indicating a larger IQR. So, Athlete A has a larger IQR.

3. (c) Which athlete went on the shortest training ride?

   • The shortest ride is the smallest value on the plot. Athlete B’s plot extends further left, showing a smaller minimum value. Thus, Athlete B went on the shortest training ride.

4. (d) Which athlete had a greater median distance?

   • The median is the line inside the box. Athlete A’s median line is further to the right, indicating a higher median distance. So, Athlete A has a greater median distance.

Would you like a more detailed explanation for any part?

Here are some related questions that might deepen your understanding:

1. What does the interquartile range (IQR) tell us about data spread?
2. How can we interpret the range and whiskers in a box plot?
3. What does it mean if the median is closer to one quartile in a box plot?
4. How can box-and-whisker plots help in comparing two datasets?
5. How would an outlier affect the box-and-whisker plot?

Tip: Box plots are great for visualizing data distribution and comparing different data sets easily by looking at ranges, medians, and spread of data.