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4024/22 Oct/Nov 2020, 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

For 80 students' times in grouped table, draw cumulative frequency graph and use it to estimate median and interquartile range; for 160 adults' errors, calculate mean, probability of more than 3 errors, and probability two selected each made exactly one error.

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

Part (ai) · 3 marks

Draw cumulative frequency diagram on grid with time 0 to 120 and cumulative frequency 0 to 80.

  1. 1Cumulative frequencies: 10, 30, 64, 76, 80
  2. 2Plot (40, 10), (60, 30), (80, 64), (100, 76), (120, 80), starting from (20, 0)
  3. 3Join with a smooth curve (or straight lines)

AnswerCorrect cumulative frequency diagram

Part (aiia) · 1 mark

Use the cumulative frequency diagram to estimate the median time.

  1. 1Median: read across from CF = 40 (half of 80)
  2. 2Median ≈ 66 minutes

Answer66 (accept 64 to 68)

Part (aiib) · 2 marks

Use the diagram to estimate the interquartile range of times.

  1. 1Lower quartile at CF = 20: ≈ 50 minutes
  2. 2Upper quartile at CF = 60: ≈ 77.6 minutes
  3. 3IQR ≈ 77.6 − 50 = 27.6 minutes

Answer24 to 28

Part (bi) · 2 marks

Calculate the mean number of errors for the 160 adults from the frequency table.

  1. 1Σfx = 0 × 24 + 1 × 30 + 2 × 50 + 3 × 32 + 4 × 16 + 5 × 8 = 330
  2. 2Mean = 330 ÷ 160 = 2.0625

Answer2.0625 or 2.063 or 2 1/16

Part (bii) · 1 mark

Find the probability a randomly selected adult made more than 3 errors.

  1. 1More than 3 errors: 16 + 8 = 24 adults
  2. 2P = 24/160

Answer24/160

Part (biii) · 2 marks

Find the probability that two randomly selected adults each made exactly one error.

  1. 1P = 30/160 × 29/159 = 870/25 440
  2. 2= 29/848

Answer29/848

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