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0580/42 Oct/Nov 2021, Question 2: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 16 marks

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The question, in short

From a cumulative frequency curve for 80 houses' floor areas, estimate median, lower quartile, interquartile range and count above 120 m², then use a frequency table for mean, histogram and a probability.

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

Part (ai) · 1 mark

Read the median floor area from the cumulative frequency curve at cumulative frequency 40.

  1. 1Median at cumulative frequency 80/2 = 40
  2. 2Read across at 40: median ≈ 90 m²

Answer90

Part (aii) · 1 mark

Read the lower quartile floor area from the curve at cumulative frequency 20.

  1. 1Lower quartile at cumulative frequency 80/4 = 20
  2. 2Read across at 20: LQ ≈ 68 m²

Answer68

Part (aiii) · 1 mark

Find the interquartile range using the upper and lower quartiles from the curve.

  1. 1Upper quartile at cumulative frequency 60: UQ ≈ 120 m²
  2. 2IQR = 120 − 68 = 52 m²

Answer52

Part (aiv) · 2 marks

Use the curve to estimate how many houses have floor area greater than 120 m².

  1. 1At a = 120 the cumulative frequency is 60
  2. 2Houses greater than 120 m² = 80 − 60 = 20

Answer20

Part (bi) · 4 marks

Calculate an estimated mean floor area from the grouped frequency table using midpoints.

  1. 1Mid-points: 50, 70, 90, 115, 145, 180
  2. 2Σfm = 14×50 + 17×70 + 18×90 + 15×115 + 9×145 + 7×180
  3. 3= 700 + 1190 + 1620 + 1725 + 1305 + 1260 = 7800
  4. 4Mean = 7800 ÷ 80 = 97.5 m²

Answer97.5

Part (bii) · 4 marks

Complete the histogram by drawing bars for the remaining floor area intervals using frequency density.

  1. 1Frequency density = frequency ÷ class width
  2. 280−100: 18 ÷ 20 = 0.9; 100−130: 15 ÷ 30 = 0.5
  3. 3130−160: 9 ÷ 30 = 0.3; 160−200: 7 ÷ 40 = 0.175
  4. 4Draw each bar to that height across its full class width

AnswerBars with heights 0.9, 0.5, 0.3, 0.175 and with correct widths

Part (biii) · 3 marks

Find the probability that two randomly chosen houses are one over 130 m² and one 60 m² or less.

  1. 1Greater than 130 m²: 9 + 7 = 16 houses; 60 m² or less: 14 houses
  2. 2P = 2 × 16/80 × 14/79 (either order)
  3. 3= 448/6320 = 28/395

Answer28/395

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Also searched as: 0580/42/O/N/21 · 0580_w21_qp_42 · 0580 w21 42 · question 2.
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