1. **State the problem:** We are given a stem-and-leaf plot and need to find the five number summary: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. 2. **List the data points:** From the stem-and-leaf plot: - 7 | 0 2 3 7 8 9 corresponds to 70, 72, 73, 77, 78, 79 - 8 | 1 5 6 9 corresponds to 81, 85, 86, 89 - 9 | 0 1 2 2 6 6 6 6 7 8 corresponds to 90, 91, 92, 92, 96, 96, 96, 96, 97, 98 3. **Order the data:** The data in ascending order is: $$70, 72, 73, 77, 78, 79, 81, 85, 86, 89, 90, 91, 92, 92, 96, 96, 96, 96, 97, 98$$ 4. **Count the data points:** There are 20 data points. 5. **Find the minimum and maximum:** Given as 70 and 98. 6. **Find the median (Q2):** Since there are 20 points (even number), median is average of 10th and 11th values. - 10th value: 89 - 11th value: 90 $$\text{Median} = \frac{89 + 90}{2} = 89.5$$ 7. **Find the lower quartile (Q1):** Median of the lower half (first 10 values): $$70, 72, 73, 77, 78, 79, 81, 85, 86, 89$$ Median of these 10 values is average of 5th and 6th: - 5th: 78 - 6th: 79 $$Q1 = \frac{78 + 79}{2} = 78.5$$ 8. **Find the upper quartile (Q3):** Median of the upper half (last 10 values): $$90, 91, 92, 92, 96, 96, 96, 96, 97, 98$$ Median is average of 5th and 6th: - 5th: 96 - 6th: 96 $$Q3 = \frac{96 + 96}{2} = 96$$ **Final five number summary:** - Minimum: 70 - Lower quartile (Q1): 78.5 - Median (Q2): 89.5 - Upper quartile (Q3): 96 - Maximum: 98