1. The problem is to find the first quartile (Q1) and third quartile (Q3) for the given data set and verify the five-number summary. 2. The data set sorted from least to greatest is: 5, 15, 15, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5. However, the user listed 10 data points, so we consider the 10 points: 15, 15, 5, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5. Sorting these 10 points gives: 5, 15, 15, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5. But since the user states n=10, we exclude the 5 or clarify the data points as 15, 15, 5, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5 (11 points). We will assume the data points are 15, 15, 5, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5 (11 points) for calculation. 3. Since the user states n=10, we will use the 10 data points: 15, 15, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5 sorted as: 15, 15, 17, 18.5, 19, 19.5, 20, 23, 24, 29.5. 4. The minimum is 15 and maximum is 29.5, which matches the summary. 5. The median (Q2) is the average of the 5th and 6th numbers: $$\frac{19 + 19.5}{2} = 19.25$$ which matches the summary. 6. To find Q1 (first quartile), find the median of the lower half (first 5 numbers): 15, 15, 17, 18.5, 19. 7. The median of these 5 numbers is the 3rd number: 17, so $$Q1 = 17$$. 8. To find Q3 (third quartile), find the median of the upper half (last 5 numbers): 19.5, 20, 23, 24, 29.5. 9. The median of these 5 numbers is the 3rd number: 23, so $$Q3 = 23$$. 10. Therefore, the five-number summary is: - Minimum: 15 - Q1: 17 - Median (Q2): 19.25 - Q3: 23 - Maximum: 29.5 11. The user's minimum, maximum, and median are correct, but Q1 and Q3 were missing and are now calculated. 12. The box plot vertical lines at 15, 17, 19.25, 23, and 29.5 correctly represent the five-number summary. Final answer: $$Q1 = 17, \quad Q3 = 23$$