1. **State the problem:** We need to construct a box-and-whisker plot for the data set: 3, 9, 10, 2, 6, 7, 5, 8, 6, 6, 4, 9, 22, and identify any outliers. 2. **Order the data:** Sort the data from smallest to largest: $$2, 3, 4, 5, 6, 6, 6, 7, 8, 9, 9, 10, 22$$ 3. **Find the median (Q2):** The median is the middle value. There are 13 data points, so the median is the 7th value: $$Q2 = 6$$ 4. **Find the lower quartile (Q1):** The lower half is the first 6 values: $$2, 3, 4, 5, 6, 6$$ Median of these is average of 3rd and 4th values: $$Q1 = \frac{4 + 5}{2} = 4.5$$ 5. **Find the upper quartile (Q3):** The upper half is the last 6 values: $$6, 7, 8, 9, 9, 10$$ Median of these is average of 3rd and 4th values: $$Q3 = \frac{8 + 9}{2} = 8.5$$ 6. **Calculate the interquartile range (IQR):** $$IQR = Q3 - Q1 = 8.5 - 4.5 = 4$$ 7. **Determine outlier boundaries:** - Lower bound: $$Q1 - 1.5 \times IQR = 4.5 - 1.5 \times 4 = 4.5 - 6 = -1.5$$ - Upper bound: $$Q3 + 1.5 \times IQR = 8.5 + 6 = 14.5$$ 8. **Identify outliers:** Any data point below -1.5 or above 14.5 is an outlier. The only value above 14.5 is 22, so 22 is an outlier. 9. **Summary for box plot:** - Minimum (non-outlier): 2 - Q1: 4.5 - Median: 6 - Q3: 8.5 - Maximum (non-outlier): 10 - Outlier: 22 This completes the box-and-whisker plot construction and outlier identification.