1. **State the problem:** We have a list of student numbers in 9 schools: 103, 229, 253, 275, 300, 310, 326, 358, 366. We want to find how changing the smallest number from 103 to 202 affects the median and mean. 2. **Recall definitions:** - The **median** is the middle value in an ordered list. - The **mean** is the sum of all values divided by the number of values. 3. **Find the original median:** Since there are 9 numbers, the median is the 5th number. Original median = 300. 4. **Find the new list after change:** Replace 103 with 202 and reorder: 202, 229, 253, 275, 300, 310, 326, 358, 366. 5. **Find the new median:** The 5th number is still 300. 6. **Conclusion for median:** The median stays the same. 7. **Calculate original mean:** $$\text{Original sum} = 103 + 229 + 253 + 275 + 300 + 310 + 326 + 358 + 366 = 2520$$ $$\text{Original mean} = \frac{2520}{9} = 280$$ 8. **Calculate new mean:** $$\text{New sum} = 202 + 229 + 253 + 275 + 300 + 310 + 326 + 358 + 366 = 2619$$ $$\text{New mean} = \frac{2619}{9} = 291$$ 9. **Change in mean:** $$291 - 280 = 11$$ 10. **Conclusion for mean:** The mean increases by 11. **Final answers:** (a) Median stays the same. (b) Mean increases by 11.