1. **State the problem:** We need to estimate the total weight of all the suitcases using the histogram data. 2. **Understand the histogram:** The histogram shows frequency density on the y-axis and weight intervals on the x-axis. 3. **Calculate the frequency for each weight interval:** Frequency = frequency density \( \times \) class width. - For 1 to 3 kg: height = 3, width = 3 - 1 = 2, frequency = 3 \times 2 = 6 - For 3 to 4 kg: height = 5, width = 4 - 3 = 1, frequency = 5 \times 1 = 5 - For 4 to 7 kg: height = 1, width = 7 - 4 = 3, frequency = 1 \times 3 = 3 4. **Estimate the midpoint weight for each interval:** - 1 to 3 kg midpoint = \( \frac{1+3}{2} = 2 \) - 3 to 4 kg midpoint = \( \frac{3+4}{2} = 3.5 \) - 4 to 7 kg midpoint = \( \frac{4+7}{2} = 5.5 \) 5. **Calculate the total weight estimate for each interval:** Total weight = frequency \( \times \) midpoint - 1 to 3 kg: 6 \times 2 = 12 - 3 to 4 kg: 5 \times 3.5 = 17.5 - 4 to 7 kg: 3 \times 5.5 = 16.5 6. **Sum all total weights:** $$12 + 17.5 + 16.5 = 46$$ 7. **Final answer:** The estimated total weight of all the suitcases is **46.0 kg** (to 1 decimal place).