Five Number Summary 914F66

1. **State the problem:** We need to find the five-number summary (minimum, first quartile Q1, median, third quartile Q3, and maximum) for the data set: $$2, 3, 5, 5, 8, 10, 12, 15, 18, 21$$. 2. **Arrange the data in order:** The data is already sorted. 3. **Find the minimum and maximum:** - Minimum is the smallest value: $$\min = 2$$. - Maximum is the largest value: $$\max = 21$$. 4. **Find the median:** - There are 10 data points (even number). - Median is the average of the 5th and 6th values. - 5th value = $$8$$, 6th value = $$10$$. - Median $$= \frac{8 + 10}{2} = \frac{18}{2} = 9$$. 5. **Find Q1 (first quartile):** - Q1 is the median of the lower half (first 5 values): $$2, 3, 5, 5, 8$$. - Median of these 5 values is the 3rd value: $$5$$. 6. **Find Q3 (third quartile):** - Q3 is the median of the upper half (last 5 values): $$10, 12, 15, 18, 21$$. - Median of these 5 values is the 3rd value: $$15$$. **Final five-number summary:** $$\min = 2, \quad Q1 = 5, \quad \text{median} = 9, \quad Q3 = 15, \quad \max = 21$$