1. **Problem Statement:** We have a sample of 15 waiting times in minutes: 1.38, 2.34, 3.02, 3.20, 3.54, 3.79, 4.21, 4.50, 4.77, 5, 5.13, 5.35, 5.55, 6.10, 6.19. We need to construct a box plot and interpret it. 2. **Step 1: Order the data** (already ordered): 1.38, 2.34, 3.02, 3.20, 3.54, 3.79, 4.21, 4.50, 4.77, 5, 5.13, 5.35, 5.55, 6.10, 6.19 3. **Step 2: Find the median (Q2):** Since there are 15 data points, median is the 8th value. $$Q2 = 4.50$$ 4. **Step 3: Find the first quartile (Q1):** Median of the lower half (first 7 values): 1.38, 2.34, 3.02, 3.20, 3.54, 3.79, 4.21 Median is the 4th value: $$Q1 = 3.20$$ 5. **Step 4: Find the third quartile (Q3):** Median of the upper half (last 7 values): 4.77, 5, 5.13, 5.35, 5.55, 6.10, 6.19 Median is the 4th value: $$Q3 = 5.35$$ 6. **Step 5: Calculate the interquartile range (IQR):** $$IQR = Q3 - Q1 = 5.35 - 3.20 = 2.15$$ 7. **Step 6: Determine the whiskers:** - Lower whisker: smallest data point greater than or equal to $$Q1 - 1.5 \times IQR = 3.20 - 1.5 \times 2.15 = 3.20 - 3.225 = -0.025$$, so minimum is 1.38 - Upper whisker: largest data point less than or equal to $$Q3 + 1.5 \times IQR = 5.35 + 3.225 = 8.575$$, so maximum is 6.19 8. **Step 7: Construct the box plot:** - Box from $$Q1 = 3.20$$ to $$Q3 = 5.35$$ - Median line at $$4.50$$ - Whiskers from $$1.38$$ to $$6.19$$ 9. **Interpretation:** - The median waiting time is 4.50 minutes. - 50% of customers wait between 3.20 and 5.35 minutes. - The waiting times are fairly spread out with an IQR of 2.15 minutes. - No outliers are detected since all data points lie within the whiskers. - The distribution is slightly skewed to the right as the upper whisker is longer than the lower whisker. Final answer: Median = 4.50, Q1 = 3.20, Q3 = 5.35, Min = 1.38, Max = 6.19, IQR = 2.15, no outliers, slight right skew.