1. **State the problem:** We have data on the number of cigarettes smoked per day by 20 patients: 10, 8, 6, 14, 22, 13, 17, 19, 11, 9, 18, 14, 13, 12, 15, 15, 5, 11, 16, 11. 2. **Goal:** Construct a frequency distribution with six classes. 3. **Step 1: Find the range of the data.** - Minimum value $= 5$ - Maximum value $= 22$ - Range $= 22 - 5 = 17$ 4. **Step 2: Determine class width.** - Number of classes $= 6$ - Class width $= \frac{\text{Range}}{\text{Number of classes}} = \frac{17}{6} \approx 2.83$ - Round up to 3 for simplicity. 5. **Step 3: Define class intervals starting from minimum value 5:** - Class 1: 5 to 7 - Class 2: 8 to 10 - Class 3: 11 to 13 - Class 4: 14 to 16 - Class 5: 17 to 19 - Class 6: 20 to 22 6. **Step 4: Tally frequencies for each class:** - Class 1 (5-7): 5, 6 → Frequency = 2 - Class 2 (8-10): 8, 9, 10 → Frequency = 3 - Class 3 (11-13): 11, 11, 11, 12, 13, 13 → Frequency = 6 - Class 4 (14-16): 14, 14, 15, 15, 16 → Frequency = 5 - Class 5 (17-19): 17, 18, 19 → Frequency = 3 - Class 6 (20-22): 22 → Frequency = 1 7. **Step 5: Present the frequency distribution table:** | Class Interval | Frequency | |----------------|-----------| | 5 - 7 | 2 | | 8 - 10 | 3 | | 11 - 13 | 6 | | 14 - 16 | 5 | | 17 - 19 | 3 | | 20 - 22 | 1 | This frequency distribution summarizes the data into six classes with their respective frequencies.