Let’s examine each question in relation to the box-and-whisker plot provided:

(a) Which athlete had a smaller range of distances?

• The range is the difference between the maximum and minimum values in each dataset.
• Athlete A has a wider range from approximately 5 to 45 miles.
• Athlete B's range is from around 10 to 40 miles.
• Therefore, Athlete B has a smaller range of distances.

(b) Which athlete had a greater median distance?

• The median is the middle line in the box of each plot.
• Athlete A’s median appears to be around 30 miles, while Athlete B’s median is approximately 20 miles.
• Hence, Athlete A has a greater median distance.

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

• The IQR is the length of the box, representing the middle 50% of data.
• Athlete A’s IQR appears to be wider than Athlete B’s.
• Consequently, Athlete A has a larger interquartile range.

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

• The shortest distance is represented by the leftmost whisker of each plot.
• Athlete A's shortest ride is around 5 miles, which is shorter than Athlete B’s shortest ride at approximately 10 miles.
• So, Athlete A went on the shortest training ride.

Would you like further details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you calculate the interquartile range (IQR) using a box-and-whisker plot?
2. Why is the median a better measure than the mean in skewed data distributions?
3. What are the advantages of using a box-and-whisker plot to represent data?
4. How do outliers affect the range and IQR in data analysis?
5. Can two datasets have the same range but different IQRs?

Tip: Always look at the IQR and range separately in box plots; they reveal different aspects of data spread and concentration.