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4MA1/2HR Jan 2023, Question 17: Histograms (Unequal Class Intervals)

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 5 marks

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The question, in short

Using a grouped frequency table of homework times, draw a histogram and estimate a probability for a randomly chosen student from specified time groups.

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

Part (a) · 3 marks

Draw a histogram on the grid using the given time intervals and frequencies, with frequency density on the vertical axis.

  1. 115 ÷ 15 = 1
  2. 218 ÷ 5 = 3.6
  3. 332 ÷ 20 = 1.6
  4. 44 ÷ 10 = 0.4
  5. 5Plot bars with heights 1, 3.6, 1.6, 0.4 and widths matching intervals

AnswerBars at frequency density 1 from 10 to 25, 3.6 from 25 to 30, 1.6 from 30 to 50 and 0.4 from 50 to 60

Part (b) · 2 marks

For a student taking over 25 and up to 50 minutes, estimate the probability they took 45 minutes or less.

  1. 1Number of students who took more than 25 minutes and 50 minutes or less: 18 + 32 = 50
  2. 2Estimate number of students who took between 30 and 45 minutes: (15/20) × 32 = 24
  3. 3Total who took between 25 and 45 minutes: 18 + 24 = 42
  4. 4Probability = 42 / 50

Answer42/50

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