1. **State the problem:** We have 20 years of rainfall data in inches and need to find the quartiles, specifically the first quartile (Q1), median (Q2), and third quartile (Q3). 2. **Recall the quartile formula:** Quartiles divide data into four equal parts. For a data set of size $n$, the position of Q1 is at $\frac{n+1}{4}$, Q2 (median) at $\frac{n+1}{2}$, and Q3 at $\frac{3(n+1)}{4}$. 3. **Calculate positions:** Here, $n=20$. $$Q1\text{ position} = \frac{20+1}{4} = \frac{21}{4} = 5.25$$ $$Q2\text{ position} = \frac{21}{2} = 10.5$$ $$Q3\text{ position} = \frac{3 \times 21}{4} = \frac{63}{4} = 15.75$$ 4. **Find Q1:** The 5.25th value lies between the 5th and 6th data points. 5th data point = 2.01, 6th data point = 2.13 Interpolate: $$Q1 = 2.01 + 0.25 \times (2.13 - 2.01) = 2.01 + 0.25 \times 0.12 = 2.01 + 0.03 = 2.04$$ 5. **Find Q2 (median):** Between 10th and 11th data points. 10th = 3.24, 11th = 3.53 $$Q2 = 3.24 + 0.5 \times (3.53 - 3.24) = 3.24 + 0.5 \times 0.29 = 3.24 + 0.145 = 3.385$$ 6. **Find Q3:** Between 15th and 16th data points. 15th = 4.87, 16th = 5.02 $$Q3 = 4.87 + 0.75 \times (5.02 - 4.87) = 4.87 + 0.75 \times 0.15 = 4.87 + 0.1125 = 4.9825$$ 7. **Final answer:** $$Q1 = 2.04, \quad Q2 = 3.385, \quad Q3 = 4.9825$$