4MA1/1HR Jun 2022, Question 19: Histograms (Unequal Class Intervals)
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
Use the histogram of tree heights and the given comparison between two class intervals to estimate how many trees are taller than 500 cm.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1The frequency density axis has no scale, so use the information given to find what one grid square is worth.
- 2On the grid each large square is 50 cm wide.
- 3Bar heights, in large squares: 200 to 250 is 5, 250 to 300 is 4, 300 to 400 is 3, 400 to 450 is 7.5, 450 to 600 is 2.5, 600 to 800 is 0.5
- 4Area of the bar for 300 < h ≤ 400 = 2 × 3 = 6 large squares
- 5Area for 400 < h ≤ 500 = 1 × 7.5 + 1 × 2.5 = 10 large squares
- 6300 < h ≤ 400 has 8 fewer trees than 400 < h ≤ 500, so 10 − 6 = 4 large squares represent 8 trees
- 71 large square represents 8 ÷ 4 = 2 trees
- 8Area for 500 < h ≤ 600 = 2 × 2.5 = 5 large squares
- 9Area for 600 < h ≤ 800 = 4 × 0.5 = 2 large squares
- 10Total area for h > 500 = 5 + 2 = 7 large squares
- 11Number of trees = 7 × 2 = 14
Answer14
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