1. **State the problem:** We are given a grouped frequency distribution of electrical cord lengths for 80 kettles and need to complete the cumulative frequency table. 2. **Recall the cumulative frequency concept:** Cumulative frequency at a class boundary is the sum of all frequencies for classes up to that boundary. 3. **Given data:** - Length intervals: 49-53, 54-58, 59-63, 64-68 - Frequencies: 11, 34, 30, 5 - Total kettles: 80 - Cumulative frequency at <53.5 is 11 4. **Calculate cumulative frequencies:** - At <58.5: sum of frequencies for 49-53 and 54-58 $$11 + 34 = 45$$ - At <63.5: sum of frequencies for 49-53, 54-58, and 59-63 $$11 + 34 + 30 = 75$$ - At <68.5: sum of all frequencies $$11 + 34 + 30 + 5 = 80$$ 5. **Complete the table:** | Length (cm) | <48.5 | <53.5 | <58.5 | <63.5 | <68.5 | |----------------------|-------|-------|-------|-------|-------| | Cumulative frequency | 0 | 11 | 45 | 75 | 80 | **Final answer:** The cumulative frequencies are 45, 75, and 80 for <58.5, <63.5, and <68.5 respectively.