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4024/21 Oct/Nov 2020, Question 2: Finding the Median and Quartiles

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 13 marks

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The question, in short

Use a cumulative frequency graph for 60 variety A potatoes, compare spread with variety B, estimate a mean from a grouped table for variety C, and find an upper bound for a box of 10 bags.

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

Part (aia) · 1 mark

Read off the mass at cumulative frequency 30 to estimate the median.

  1. 1Median at cumulative frequency 60 ÷ 2 = 30
  2. 2Read across at 30 to the curve and down: 188 g

Answer188 to 189

Part (aib) · 2 marks

Use the graph to find the lower and upper quartiles, then work out the interquartile range.

  1. 1Lower quartile at 15: about 170 g
  2. 2Upper quartile at 45: about 208 g
  3. 3IQR = 208 − 170 = 38 g

Answer37 to 39

Part (aii) · 3 marks

Find how many potatoes exceed 220 g and express this as a percentage of 60.

  1. 1At 220 g the cumulative frequency is 52
  2. 2Number heavier than 220 g = 60 − 52 = 8
  3. 3Percentage = 8/60 × 100 = 13.3%

Answer13.3

Part (aiii) · 1 mark

Compare the interquartile ranges of A and B to decide which variety has masses closer together.

  1. 1IQR for A ≈ 38 g, IQR for B = 30 g
  2. 2B has the smaller interquartile range, so its masses are more consistent: variety B

AnswerB, IQR is smaller

Part (b) · 3 marks

Using midpoints of the mass classes and their frequencies, estimate the mean mass of the 120 potatoes.

  1. 1Midpoints: 90, 110, 125, 135, 170
  2. 2Σfx = 900 + 1650 + 5250 + 4860 + 2890 = 15 550
  3. 3Mean = 15 550 ÷ 120 = 129.6 g

Answer130 or 129.5 to 129.6

Part (c) · 3 marks

With 2.5 kg to the nearest 100 g and box 600 g to the nearest 10 g, find the upper bound for 10 bags plus the box, in kg.

  1. 1Upper bound of one bag = 2.55 kg
  2. 2Upper bound of box = 605 g = 0.605 kg
  3. 3Total = 10 × 2.55 + 0.605 = 26.105 kg

Answer26.105

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Also searched as: 4024/21/O/N/20 · 4024_w20_qp_21 · 4024 w20 21 · question 2.
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