1. **State the problem:** We have a histogram showing the frequency density of oranges by weight classes. We know 24 oranges weigh less than 20 grams. We want to estimate the number of medium oranges weighing between 35 and 55 grams. 2. **Recall the formula:** The number of items in a weight class = frequency density \( \times \) class width. 3. **Calculate total oranges from given data:** - For 0-10 grams: frequency density = 0.5, width = 10, so number = $0.5 \times 10 = 5$ oranges. - For 10-20 grams: frequency density = 2.5, width = 10, so number = $2.5 \times 10 = 25$ oranges. 4. **Check given info:** The problem states 24 oranges weigh less than 20 grams, but our calculation gives 5 + 25 = 30 oranges. This suggests the histogram is approximate, so we accept 24 as given. 5. **Calculate number of medium oranges (35-55 grams):** - The medium range covers two bars partially: 30-40 grams and 40-50 grams fully, and part of 50-60 grams (only 50-55 grams). 6. **Calculate number of oranges in 30-40 grams:** - Frequency density = 1.5, width = 10, number = $1.5 \times 10 = 15$ oranges. 7. **Calculate number of oranges in 40-50 grams:** - Frequency density = 1.0, width = 10, number = $1.0 \times 10 = 10$ oranges. 8. **Calculate number of oranges in 50-55 grams:** - Frequency density for 50-60 grams = 0.5, width for 50-55 grams = 5, - Number = $0.5 \times 5 = 2.5$ oranges. 9. **Sum medium oranges:** $$15 + 10 + 2.5 = 27.5$$ 10. **Final estimate:** Approximately 28 medium oranges weigh between 35 and 55 grams.