1. **Stating the problem:** We have a dataset of absences over 18 days: 4, 3, 0, 1, 2, 5, 6, 8, 10, 7, 11, 15, 19, 13, 4, 2, 12. 2. **Goal:** To create a frequency distribution with continuous class intervals and understand the histogram shape. 3. **Step 1: Determine the range of data.** - Minimum value: $0$ - Maximum value: $19$ - Range: $19 - 0 = 19$ 4. **Step 2: Decide the number of classes.** - A common rule is to use between 5 and 10 classes. - Let's choose 6 classes for clarity. 5. **Step 3: Calculate class width.** - Class width $= \frac{\text{Range}}{\text{Number of classes}} = \frac{19}{6} \approx 3.17$ - Round up to $4$ for simplicity. 6. **Step 4: Define class intervals starting from 0:** - Class 1: $0 - 3$ - Class 2: $4 - 7$ - Class 3: $8 - 11$ - Class 4: $12 - 15$ - Class 5: $16 - 19$ 7. **Step 5: Tally frequencies:** - Class 1 (0-3): values $0,1,2,2,3$ → frequency $5$ - Class 2 (4-7): values $4,4,5,6,7$ → frequency $5$ - Class 3 (8-11): values $8,10,11$ → frequency $3$ - Class 4 (12-15): values $12,13,15$ → frequency $3$ - Class 5 (16-19): values $19$ → frequency $1$ 8. **Step 6: Interpret histogram shape:** - Frequencies rise to a peak around classes 1 and 2 (frequency 5), then decrease. - This matches the description of bars rising to a peak and then descending. **Final frequency distribution table:** | Class Interval | Frequency | |---------------|-----------| | 0 - 3 | 5 | | 4 - 7 | 5 | | 8 - 11 | 3 | | 12 - 15 | 3 | | 16 - 19 | 1 | This distribution explains the histogram's shape with frequencies peaking around 5 and then decreasing.