Let's carefully analyze the box-and-whisker plots for Athlete A and Athlete B and answer the questions:

Key Observations:

• Median: Represented by the line inside each box. Compare positions of the lines for Athlete A and Athlete B.
• Range: This is the distance between the smallest value (left whisker) and the largest value (right whisker).
• Interquartile Range (IQR): The length of the box itself (distance between the 1st quartile $Q_1$ and the 3rd quartile $Q_3$).
• Shortest Ride: Determined by the position of the leftmost whisker (smallest value).

Answers:

1. (a) Which athlete had a greater median distance?

   • Athlete A has a greater median.
     Explanation: The median line for Athlete A is further to the right than for Athlete B.

2. (b) Which athlete had a smaller range of distances?

   • Athlete B had a smaller range.
     Explanation: The distance between the left and right whiskers for Athlete B is shorter compared to Athlete A.

3. (c) Which athlete had distances with a larger interquartile range (IQR)?

   • Athlete A had a larger IQR.
     Explanation: The box (IQR) for Athlete A is wider than the box for Athlete B.

4. (d) Which athlete went on the shortest training ride?

   • Athlete B went on the shortest training ride.
     Explanation: The leftmost whisker (minimum value) for Athlete B is further to the left compared to Athlete A.

Let me know if you would like any further clarifications or a detailed explanation for each answer!

Related Questions:

1. How do you calculate the exact interquartile range (IQR) for a dataset?
2. What does the range of a dataset tell us about its variability?
3. Why is the median more robust to outliers compared to the mean?
4. How can box-and-whisker plots help compare two data distributions?
5. What does it mean when two box plots have similar medians but different IQRs?

Tip: In a box plot, the whiskers show the spread of the data, while the box represents the middle 50% of the data (IQR). Always compare whisker lengths and box widths for variability!