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4MA1/1H Jun 2023, Question 18: Histograms (Unequal Class Intervals)

Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks

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The question, in short

Using the incomplete table and histogram for 140 people's waiting times, find the missing frequencies and complete both the table and the histogram.

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

Solution · 4 marks

  1. 1The two missing frequencies add up to 140 − 23 − 18 − 14 = 85
  2. 2On the histogram the two drawn bars cover 34 cm squares altogether
  3. 3So 1 cm square stands for 85 ÷ 34 = 2.5 people
  4. 4The 5 to 15 bar covers 10 cm squares, so its frequency is 10 × 2.5 = 25
  5. 5The 15 to 30 bar covers 24 cm squares, so its frequency is 24 × 2.5 = 60
  6. 6For the missing bars, frequency density = frequency ÷ width
  7. 70 to 5: 23 ÷ 5 = 4.6; 30 to 40: 18 ÷ 10 = 1.8; 40 to 60: 14 ÷ 20 = 0.7

Answer5 < t ≤ 15 is 25 and 15 < t ≤ 30 is 60; bars of frequency density 4.6, 1.8 and 0.7

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