https://file.aiquickdraw.com/mathbot/file/1727652805654yz76u0zt.jpg

Let's analyze the box-and-whisker plots to answer the questions based on the image you've uploaded:

1. **(a) Which athlete had a smaller range of distances?**
   - The range is determined by the distance between the minimum and maximum values (whiskers). 
   - **Athlete A** has a range from about 10 miles to 40 miles, while **Athlete B** has a range from around 15 miles to 45 miles.
   - **Answer**: Athlete A had a smaller range of distances.

2. **(b) Which athlete had distances with a larger interquartile range (IQR)?**
   - The IQR is the distance between the first quartile (Q1) and the third quartile (Q3), represented by the width of the box in the plot.
   - **Athlete B** has a visibly larger box, indicating a larger IQR compared to **Athlete A**.
   - **Answer**: Athlete B had a larger IQR.

3. **(c) Which athlete went on the shortest training ride?**
   - The shortest ride is indicated by the smallest value (left-most point of the whisker).
   - **Athlete A**'s shortest ride is approximately 10 miles, while **Athlete B**'s shortest ride is around 15 miles.
   - **Answer**: Athlete A went on the shortest training ride.

4. **(d) Which athlete had a greater median distance?**
   - The median is represented by the line inside the box.
   - **Athlete A**'s median is around 30 miles, while **Athlete B**'s median is around 25 miles.
   - **Answer**: Athlete A had a greater median distance.

Let me know if you need any further clarifications or a deeper explanation of box-and-whisker plots!

Here are five related questions to consider:
1. What does the length of the whiskers tell us about the data distribution?
2. How can outliers affect the interpretation of the box plot?
3. Why is the median a better measure of central tendency than the mean in certain datasets?
4. How would you calculate the interquartile range (IQR) from raw data?
5. In what types of real-world situations would box plots be especially useful?

**Tip**: A box-and-whisker plot is great for quickly visualizing data spread, central tendency, and potential outliers!

Two athletes are training for a cycling race. Each athlete recorded the distance (in miles) of their previous 95 training rides. Use the box-and-whisker plots to answer the questions about their training data.

Analyze box-and-whisker plots to compare the cycling distances of two athletes. Understand key statistical concepts like range, interquartile range (IQR), and median. This exercise helps in visualizing data spread and central tendencies, suitable for students in Grades 6-8.

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