1. **State the problem:** We need to find the outlier in the data set: 35, 25, 29, 42, 11, 34, 18, 87, 10, 24. 2. **Explain the concept:** An outlier is a value that is significantly different from the other values in the data set. One common method to detect outliers is to use the Interquartile Range (IQR). 3. **Calculate the quartiles:** - Sort the data: 10, 11, 18, 24, 25, 29, 34, 35, 42, 87 - Median (Q2) is the average of 25 and 29: $$\frac{25 + 29}{2} = 27$$ - Lower quartile (Q1) is median of lower half: 10, 11, 18, 24, 25 → median is 18 - Upper quartile (Q3) is median of upper half: 29, 34, 35, 42, 87 → median is 35 4. **Calculate IQR:** $$IQR = Q3 - Q1 = 35 - 18 = 17$$ 5. **Determine outlier boundaries:** - Lower bound: $$Q1 - 1.5 \times IQR = 18 - 1.5 \times 17 = 18 - 25.5 = -7.5$$ - Upper bound: $$Q3 + 1.5 \times IQR = 35 + 1.5 \times 17 = 35 + 25.5 = 60.5$$ 6. **Identify outliers:** - Any data point less than -7.5 or greater than 60.5 is an outlier. - The only value greater than 60.5 is 87. **Final answer:** The outlier in the data set is **87**.