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4MA1/2H Jan 2023, Question 18: Histograms (Unequal Class Intervals)

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

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The question, in short

From a grouped frequency table of parcel weights in kg, draw a histogram on the given grid and estimate a probability for a randomly chosen parcel.

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 grouped weights and frequencies, with frequency density on the vertical axis.

  1. 1Frequency densities: 12 ÷ 2 = 6
  2. 27 ÷ 1 = 7
  3. 315 ÷ 3 = 5
  4. 412 ÷ 3 = 4
  5. 59 ÷ 5 = 1.8
  6. 6Draw bars with correct widths and heights corresponding to fd 6, 7, 5, 4, 1.8

AnswerBars at frequency densities 6 from 0 to 2, 7 from 2 to 3, 5 from 3 to 6, 4 from 6 to 9 and 1.8 from 9 to 14

Part (b) · 2 marks

Estimate the probability that a randomly chosen parcel weighs more than 7 kg.

  1. 1Total frequency = 12 + 7 + 15 + 12 + 9 = 55
  2. 2Frequency for w > 7: from 6 < w ≤ 9, the part above 7 is (9 − 7)/3 × 12 = 2/3 × 12 = 8
  3. 3Plus all of 9 < w ≤ 14: 9
  4. 48 + 9 = 17
  5. 5Probability = 17/55

Answer17/55

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