1. **State the problem:** We have a data set representing the number of states traveled to or lived in: $$1, 5, 6, 2, 6, 1, 12, 7, 1, 2, 6, 1, 2, 9, 13$$ We need to find the median, mode, and range of this data (Question 9), and then determine if changing the value 5 to 8 affects the median (Question 10). 2. **Recall definitions and formulas:** - Median: The middle value when data is ordered. - Mode: The most frequently occurring value. - Range: Difference between the maximum and minimum values. 3. **Find the median, mode, and range for the original data:** - Order the data: $$1, 1, 1, 1, 2, 2, 2, 5, 6, 6, 6, 7, 9, 12, 13$$ - Median: Since there are 15 numbers (odd), median is the 8th value: $$\text{Median} = 5$$ - Mode: The value appearing most often is 1 (appears 4 times). - Range: $$13 - 1 = 12$$ 4. **Answer for Question 9:** Median = 5, Mode = 1, Range = 12 5. **For Question 10, update the data by changing 5 to 8:** New data: $$1, 8, 6, 2, 6, 1, 12, 7, 1, 2, 6, 1, 2, 9, 13$$ Order the new data: $$1, 1, 1, 1, 2, 2, 2, 6, 6, 6, 7, 8, 9, 12, 13$$ Median is the 8th value: $$\text{Median} = 6$$ 6. **Conclusion:** Yes, the median increases from 5 to 6. **Final answers:** 9. Median = 5, Mode = 1, Range = 12 10. A. Yes. It increases to 6