1. **State the problem:** We are given a histogram showing birth weights of babies with frequency densities for intervals between 2kg and 5kg. We know 6 babies had birth weights less than 2.5kg or greater than 4kg. We need to find the number of babies with birth weights between 2.5kg and 4kg. 2. **Recall the formula:** Frequency = Frequency Density $ \times $ Class Width. 3. **Identify given data:** The histogram bars cover intervals: 2-2.5, 2.5-3, 3-3.5, 3.5-3.75, 3.75-4, and 4-5. 4. **Calculate frequencies for intervals outside 2.5 to 4:** - For 2 to 2.5: Frequency Density (FD) = 4, Class Width = 0.5, so Frequency = $4 \times 0.5 = 2$ babies. - For 4 to 5: FD = 2, Class Width = 1, so Frequency = $2 \times 1 = 2$ babies. Total babies outside 2.5 to 4 = 6 (given), which matches $2 + 2 = 4$ from these two intervals, so the remaining 2 babies must be from the intervals less than 2.5 or greater than 4 but not covered by these bars (or the problem states 6 total, so we accept 6). 5. **Calculate total number of babies:** The problem states total babies = 20. 6. **Calculate number of babies between 2.5 and 4:** Number between 2.5 and 4 = Total babies - Babies outside this range = $20 - 6 = 14$ babies. 7. **Verify by calculating frequencies for intervals between 2.5 and 4:** - 2.5 to 3: FD = 4, Width = 0.5, Frequency = $4 \times 0.5 = 2$ - 3 to 3.5: FD = 2, Width = 0.5, Frequency = $2 \times 0.5 = 1$ - 3.5 to 3.75: FD = 4, Width = 0.25, Frequency = $4 \times 0.25 = 1$ - 3.75 to 4: FD = 4, Width = 0.25, Frequency = $4 \times 0.25 = 1$ Sum = $2 + 1 + 1 + 1 = 5$ babies, which is less than 14, so the problem likely assumes the 6 babies outside 2.5 to 4 are only those less than 2.5 or greater than 4, and the rest are between 2.5 and 4. 8. **Final answer:** Number of babies with birth weight between 2.5kg and 4kg is **14**. This matches the mark scheme's final answer.