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4024/22 May/Jun 2020, Question 4: Histograms (Unequal Class Intervals)

Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 11 marks

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The question, in short

Using a grouped frequency table and partial histogram of daily music-listening hours, determine a missing frequency, finish the histogram, then estimate mean cooking time, draw a cumulative frequency curve and estimate the median.

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

Part (ai) · 1 mark

Read the bar height for 1 1/2 < m ≤ 2 and use class width to work out p.

  1. 1Frequency = frequency density × width
  2. 2p = 30 × 1/2 = 15

Answer15

Part (aii) · 3 marks

Add the remaining bars to the histogram using frequency density for each class.

  1. 1Frequency densities: 14 ÷ 0.5 = 28, 23 ÷ 1 = 23, 18 ÷ 1.5 = 12, 12 ÷ 2 = 6
  2. 2Draw bars 2 to 2.5 (height 28), 2.5 to 3.5 (height 23), 3.5 to 5 (height 12), 5 to 7 (height 6)

AnswerCorrect histogram

Part (bi) · 3 marks

Estimate the mean cooking time from the grouped table of 50 students.

  1. 1Midpoints: 1, 3, 5, 7, 9
  2. 2Σfc = 1 × 8 + 3 × 16 + 5 × 15 + 7 × 7 + 9 × 4 = 8 + 48 + 75 + 49 + 36 = 216
  3. 3Mean = 216 ÷ 50 = 4.32 hours

Answer4.32

Part (bii) · 3 marks

Plot cumulative frequencies against upper class bounds and join with a smooth curve.

  1. 1Cumulative frequencies: 8, 24, 39, 46, 50
  2. 2Plot (0, 0), (2, 8), (4, 24), (6, 39), (8, 46), (10, 50)
  3. 3Join with a smooth curve

AnswerCorrect cumulative frequency curve

Part (biii) · 1 mark

Read the median cooking time from the cumulative frequency curve at 25.

  1. 1Median at cumulative frequency 50 ÷ 2 = 25
  2. 2Reading across from 25: 4 + (25 − 24)/15 × 2 ≈ 4.1 hours

Answer4 to 4.2

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Also searched as: 4024/22/M/J/20 · 4024_s20_qp_22 · 4024 s20 22 · question 4.
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