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0580/42 May/Jun 2022, Question 7: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 12 marks

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The question, in short

From a grouped frequency table of masses for 150 children, estimate the mean, draw a histogram, complete a cumulative frequency table and find a percentage above 10 kg.

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

Part (a) · 4 marks

Calculate an estimate of the mean mass using the grouped frequency table.

  1. 1Mid-values: 5, 15, 22.5, 32.5, 45
  2. 2Σfx = 12×5 + 38×15 + 32×22.5 + 50×32.5 + 18×45
  3. 3= 60 + 570 + 720 + 1625 + 810 = 3785
  4. 4Mean = 3785 ÷ 150 = 25.23… ≈ 25.2 kg

Answer25.2 or 25.23…

Part (b) · 4 marks

Draw a histogram of the data on the given axes of mass and frequency density.

  1. 1Frequency density = frequency ÷ class width
  2. 212 ÷ 10 = 1.2, 38 ÷ 10 = 3.8, 32 ÷ 5 = 6.4, 50 ÷ 15 = 3.33…, 18 ÷ 10 = 1.8
  3. 3Draw bars 0−10 (1.2), 10−20 (3.8), 20−25 (6.4), 25−40 (3.33), 40−50 (1.8) with no gaps

Answer5 correct blocks

Part (ci) · 2 marks

Complete the cumulative frequency table for the given mass intervals.

  1. 112, 12 + 38 = 50, 50 + 32 = 82, 82 + 50 = 132, 132 + 18 = 150
  2. 2Cumulative frequencies: 12, 50, 82, 132, 150

Answer| Mass (m kg) | m ≤ 10 | m ≤ 20 | m ≤ 25 | m ≤ 40 | m ≤ 50 | | Cumulative frequency | 12 | 50 | 82 | 132 | 150 |

Part (cii) · 2 marks

Calculate the percentage of children whose mass is greater than 10 kg.

  1. 1Mass > 10 kg: 150 − 12 = 138 children
  2. 2138 ÷ 150 × 100 = 92%

Answer92

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Also searched as: 0580/42/M/J/22 · 0580_s22_qp_42 · 0580 s22 42 · question 7.
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