1. **State the problem:** We are given a data set representing the number of states traveled to or lived in: 2, 3, 6, 2, 6, 1, 11, 8, 2, 1, 5, 2, 1, 7, 14. 2. **Find the median, mode, and range of the data:** - Median is the middle value when data is sorted. - Mode is the most frequent value. - Range is the difference between the maximum and minimum values. 3. **Sort the data:** $$1, 1, 1, 2, 2, 2, 2, 3, 5, 6, 6, 7, 8, 11, 14$$ 4. **Find the median:** - There are 15 data points (odd number). - Median is the 8th value. - The 8th value is $3$. 5. **Find the mode:** - Count frequencies: - 1 appears 3 times - 2 appears 4 times - Others less frequent - Mode is $2$ (most frequent). 6. **Find the range:** - Maximum value is $14$. - Minimum value is $1$. - Range = $14 - 1 = 13$. 7. **Answer for question 9:** - Median = $3$ - Mode = $2$ - Range = $13$ 8. **For question 10:** The student who traveled to 3 states now traveled to 8 states. 9. **Update the data:** Replace one $3$ with $8$: $$1, 1, 1, 2, 2, 2, 2, 5, 6, 6, 7, 8, 8, 11, 14$$ 10. **Find the new median:** - Still 15 data points. - Median is the 8th value. - The 8th value is now $5$. 11. **Compare medians:** - Original median was $3$. - New median is $5$. - Median increases. 12. **Answer for question 10:** C. Yes. It increases to 5.