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0580/43 May/Jun 2021, Question 3: Estimating the Mean for Grouped Data

Cambridge IGCSE Mathematics 0580 · Paper 43 (Extended) · Calculator · 15 marks

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The question, in short

Work with Zoe's nine scores, a cumulative frequency curve for 200 students' times, a frequency table of 200 scores, and a histogram of 200 plant heights to find averages, spread and estimates.

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

Part (ai) · 1 mark

Find the range of Zoe's nine test scores.

  1. 1Range = 10 − 6 = 4

Answer4

Part (aii) · 1 mark

Find the mode of Zoe's nine test scores.

  1. 17 appears most often (3 times): mode = 7

Answer7

Part (aiii) · 1 mark

Find the median of Zoe's nine test scores.

  1. 19 scores, so the median is the 5th: 6 7 7 7 8 … → median = 8

Answer8

Part (bi) · 1 mark

Use the cumulative frequency diagram to estimate the median time for the 200 students.

  1. 1Median at cumulative frequency 1/2 × 200 = 100
  2. 2Reading across from 100 to the curve and down: median ≈ 14 minutes

Answer14

Part (bii) · 2 marks

Use the cumulative frequency diagram to estimate the interquartile range of the times.

  1. 1Lower quartile at CF 50: 11 minutes
  2. 2Upper quartile at CF 150: 15 minutes
  3. 3IQR = 15 − 11 = 4 minutes

Answer4

Part (c) · 3 marks

Calculate the mean score from the frequency table of 200 students' scores.

  1. 1Σfx = 5×3 + 6×10 + 7×43 + 8×75 + 9×48 + 10×21
  2. 2= 15 + 60 + 301 + 600 + 432 + 210 = 1618
  3. 3Mean = 1618 ÷ 200 = 8.09

Answer8.09

Part (d) · 6 marks

Use the histogram to estimate the mean height of the 200 plants, showing all working.

  1. 1Frequencies (fd × width): 1 × 30 = 30, 3.5 × 20 = 70, 4 × 10 = 40, 3.6 × 10 = 36, 0.6 × 40 = 24
  2. 2Midpoints: 65, 90, 105, 115, 140
  3. 3Σfx = 30×65 + 70×90 + 40×105 + 36×115 + 24×140
  4. 4= 1950 + 6300 + 4200 + 4140 + 3360 = 19 950
  5. 5Mean = 19 950 ÷ 200 = 99.75 cm

Answer99.75

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Also searched as: 0580/43/M/J/21 · 0580_s21_qp_43 · 0580 s21 43 · question 3.
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