1. **State the problem:** We have a set of data values and need to group them into six classes and then find the relative frequency distribution. 2. **Find the range:** The range is the difference between the maximum and minimum values. Maximum value = 16.5 Minimum value = 3.8 Range = $16.5 - 3.8 = 12.7$ 3. **Determine class width:** Divide the range by the number of classes (6). Class width = $\frac{12.7}{6} \approx 2.12$ We round up to 2.2 for convenience. 4. **Create class intervals:** Starting from the minimum value 3.8, add class width 2.2 to form intervals: - 3.8 to 6.0 - 6.0 to 8.2 - 8.2 to 10.4 - 10.4 to 12.6 - 12.6 to 14.8 - 14.8 to 17.0 5. **Count frequencies:** Count how many data points fall into each class. - 3.8 to 6.0: 3 values (3.8, 5.9, 6.2) - 6.0 to 8.2: 5 values (7.4, 7.9, 8.1, 8.3, 8.4) - 8.2 to 10.4: 10 values (8.6, 8.8, 9.1, 9.1, 9.8, 9.9, 9.9, 10.1, 10.4, 10.5) - 10.4 to 12.6: 12 values (10.5, 10.9, 10.9, 11.2, 11.2, 11.4, 11.5, 11.5, 11.5, 11.6, 11.7, 12.3) - 12.6 to 14.8: 7 values (12.5, 12.7, 12.7, 12.9, 13.4, 13.6, 14.4) - 14.8 to 17.0: 3 values (14.7, 15.0, 16.5) 6. **Calculate relative frequencies:** Divide each class frequency by total number of data points (40). - $\frac{3}{40} = 0.075$ - $\frac{5}{40} = 0.125$ - $\frac{10}{40} = 0.25$ - $\frac{12}{40} = 0.3$ - $\frac{7}{40} = 0.175$ - $\frac{3}{40} = 0.075$ 7. **Final relative frequency distribution:** | Class Interval | Frequency | Relative Frequency | |---------------|-----------|--------------------| | 3.8 - 6.0 | 3 | 0.075 | | 6.0 - 8.2 | 5 | 0.125 | | 8.2 - 10.4 | 10 | 0.25 | | 10.4 - 12.6 | 12 | 0.3 | | 12.6 - 14.8 | 7 | 0.175 | | 14.8 - 17.0 | 3 | 0.075 |