Five Number Summary 334De8

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: $$3, 5, 6, 8, 9, 11, 12, 16, 16, 19$$. 2. **Arrange the data in order:** The data is already sorted. 3. **Identify the minimum and maximum:** - Minimum is the smallest value: $$\min = 3$$. - Maximum is the largest value: $$\max = 19$$. 4. **Find the median:** The median is the middle value. Since there are 10 data points (even number), median is the average of the 5th and 6th values. - 5th value = $$9$$ - 6th value = $$11$$ - Median $$= \frac{9 + 11}{2} = \frac{20}{2} = 10$$ 5. **Find Q1 (first quartile):** Q1 is the median of the lower half (first 5 values: $$3, 5, 6, 8, 9$$). - Median of these 5 values is the 3rd value: $$6$$ 6. **Find Q3 (third quartile):** Q3 is the median of the upper half (last 5 values: $$11, 12, 16, 16, 19$$). - Median of these 5 values is the 3rd value: $$16$$ **Final five-number summary:** $$\min = 3, \quad Q1 = 6, \quad \text{median} = 10, \quad Q3 = 16, \quad \max = 19$$