1. **State the problem:** Find the lower quartile (Q1) and upper quartile (Q3) for the data set $4, 8, 2, 7, 10$ without a calculator. 2. **Sort the data:** Arrange the numbers in ascending order: $$2, 4, 7, 8, 10$$ 3. **Find the median (Q2):** The median is the middle number in the sorted list. Here, the middle number is $7$. 4. **Find Q1 (lower quartile):** Q1 is the median of the lower half of the data (numbers before the median). The lower half is $$2, 4$$ 5. **Calculate Q1:** Since there are two numbers, Q1 is the average: $$Q1 = \frac{2 + 4}{2} = \frac{6}{2} = 3$$ 6. **Find Q3 (upper quartile):** Q3 is the median of the upper half of the data (numbers after the median). The upper half is $$8, 10$$ 7. **Calculate Q3:** Average of the two numbers: $$Q3 = \frac{8 + 10}{2} = \frac{18}{2} = 9$$ **Final answer:** $$Q1 = 3, \quad Q3 = 9$$