1. **State the problem:** Find the quartiles (Q1, Q2, Q3) for the given data set. 2. **Recall definitions:** - Q1 (first quartile) is the median of the lower half of the data (below the median). - Q2 (median) is the middle value of the data. - Q3 (third quartile) is the median of the upper half of the data (above the median). 3. **Given data set (sorted):** 5.0, 5.1, 5.2, 5.2, 5.3, 5.4, 5.5, 5.5, 5.6, 5.6, 5.7, 5.8, 5.9, 6.0, 6.2, 6.3, 6.5, 6.8, 7.0, 7.2, 7.5, 7.8, 8.3, 8.9 4. **Find the median (Q2):** - Number of data points $n=24$ (even). - Median is average of 12th and 13th values. - 12th value = 5.8, 13th value = 5.9. - Calculate median: $$Q2 = \frac{5.8 + 5.9}{2} = \frac{11.7}{2} = 5.85$$ 5. **Split data into lower and upper halves:** - Lower half (first 12 values): 5.0 to 5.8 - Upper half (last 12 values): 5.9 to 8.9 6. **Find Q1 (median of lower half):** - Lower half has 12 values. - Median is average of 6th and 7th values. - 6th value = 5.4, 7th value = 5.5. - Calculate Q1: $$Q1 = \frac{5.4 + 5.5}{2} = \frac{10.9}{2} = 5.45$$ 7. **Find Q3 (median of upper half):** - Upper half has 12 values. - Median is average of 6th and 7th values in upper half. - 6th value in upper half = 6.8, 7th value = 7.0. - Calculate Q3: $$Q3 = \frac{6.8 + 7.0}{2} = \frac{13.8}{2} = 6.9$$ 8. **Summary:** - $Q1 = 5.45$ - $Q2 = 5.85$ - $Q3 = 6.9$ **Final answer:** The quartiles are $Q1 = 5.45$, $Q2 = 5.85$, and $Q3 = 6.9$.