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, the median is the 8th value. $$\text{Median} = 4.50$$ 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 of these 7 values 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 limit: $$Q1 - 1.5 \times IQR = 3.20 - 1.5 \times 2.15 = 3.20 - 3.225 = -0.025$$ (minimum data point above this is 1.38) - Upper whisker limit: $$Q3 + 1.5 \times IQR = 5.35 + 3.225 = 8.575$$ (maximum data point below this is 6.19) 8. **Step 7: Identify outliers:** No data points below 1.38 or above 6.19, so no outliers. 9. **Step 8: Construct the box plot:** - Minimum: 1.38 - Q1: 3.20 - Median: 4.50 - Q3: 5.35 - Maximum: 6.19 10. **Interpretation:** - The median waiting time is 4.50 minutes. - 50% of customers wait between 3.20 and 5.35 minutes. - The spread (IQR) is 2.15 minutes, indicating moderate variability. - No outliers suggest consistent service times during this period. This box plot visually summarizes the distribution of waiting times, showing central tendency and variability clearly.