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4024/22 Oct/Nov 2022, Question 2: Drawing Cumulative Frequency Diagrams

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks

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The question, in short

Compare tomato counts for plant types A and B using a frequency table, and analyse strawberry masses from a grouped frequency table with a cumulative frequency diagram.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 2 marks

Calculate the mean number of tomatoes per type A plant from the frequency table.

  1. 1Σfx = 17×5 + 18×2 + 19×7 + 20×3 + 21×2 + 22×1 = 378
  2. 2Σf = 5 + 2 + 7 + 3 + 2 + 1 = 20
  3. 3Mean = 378 ÷ 20 = 18.9

Answer18.9 or 18 9/10

Part (aii) · 1 mark

Calculate the range of the number of tomatoes on type A plants.

  1. 1Range = 22 − 17 = 5

Answer5

Part (aiii) · 2 marks

Given type B mean 17.1 and range 8, make two comments comparing type A and type B tomato numbers.

  1. 1Type A mean = 378 ÷ 20 = 18.9; range = 22 − 17 = 5
  2. 2Mean: 18.9 > 17.1, so type A has more tomatoes per plant
  3. 3Range: 5 < 8, so type A is more consistent
  4. 4Type A has more tomatoes per plant; number of tomatoes per plant is more consistent for type A

AnswerType A has more tomatoes per plant; number of tomatoes per plant is more consistent for type A

Part (bi) · 3 marks

Draw a cumulative frequency diagram for the 120 strawberry masses using the grouped frequency table.

  1. 1Cumulative frequencies: 15, 53, 98, 115, 120
  2. 2Plot (5, 0), (10, 15), (15, 53), (20, 98), (25, 115), (30, 120) at the upper class boundaries
  3. 3Join with a smooth increasing curve

AnswerCorrect cumulative frequency curve

Part (bii) · 3 marks

Using your cumulative frequency diagram, estimate the percentage of strawberries with mass greater than 21 grams.

  1. 1Read the curve at m = 21: 98 + 1/5 × 17 ≈ 101.4
  2. 2More than 21 g: 120 − 101.4 = 18.6
  3. 318.6/120 × 100 = 15.5%

Answer13.3 to 15.8

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Also searched as: 4024/22/O/N/22 · 4024_w22_qp_22 · 4024 w22 22 · question 2.
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