1. **State the problem:** We are comparing two athletes' training ride distances using box-and-whisker plots to answer questions about interquartile range (IQR), shortest ride, range, and median distance. 2. **Recall definitions:** - The **interquartile range (IQR)** is the difference between the third quartile ($Q_3$) and the first quartile ($Q_1$): $$\text{IQR} = Q_3 - Q_1$$ - The **range** is the difference between the maximum and minimum values: $$\text{Range} = \text{Max} - \text{Min}$$ - The **median** is the middle value of the data set. 3. **Analyze Athlete A's boxplot:** - Approximate $Q_1 \approx 23$ miles - Approximate $Q_3 \approx 30$ miles - Minimum distance $\approx 15$ miles - Maximum distance $\approx 35$ miles - Median $\approx 27$ miles 4. **Analyze Athlete B's boxplot:** - Approximate $Q_1 \approx 18$ miles - Approximate $Q_3 \approx 32$ miles - Minimum distance $\approx 12$ miles - Maximum distance $\approx 38$ miles - Median $\approx 25$ miles 5. **Calculate IQRs:** $$\text{IQR}_A = 30 - 23 = 7$$ $$\text{IQR}_B = 32 - 18 = 14$$ 6. **Compare shortest rides:** - Athlete A shortest ride $\approx 15$ miles - Athlete B shortest ride $\approx 12$ miles 7. **Calculate ranges:** $$\text{Range}_A = 35 - 15 = 20$$ $$\text{Range}_B = 38 - 12 = 26$$ 8. **Compare medians:** - Athlete A median $\approx 27$ miles - Athlete B median $\approx 25$ miles **Final answers:** (a) Athlete B had the larger IQR. (b) Athlete B went on the shortest training ride. (c) Athlete A had the smaller range of distances. (d) Athlete A had the greater median distance.