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4024/21 May/Jun 2023, Question 4: Drawing Cumulative Frequency Diagrams

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 8 marks

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The question, in short

Using a cumulative frequency graph of fuel bought by 100 customers, estimate median and interquartile range, find a fraction spending over $91.00 at $1.75 per litre, and complete a grouped frequency table.

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

Part (ai) · 1 mark

Read the median fuel amount from the cumulative frequency curve at cumulative frequency 50.

  1. 1Median at cumulative frequency 100/2 = 50
  2. 2Read across from 50 to the curve and down: median ≈ 29 litres

Answer28 to 30

Part (aii) · 2 marks

Find the interquartile range by reading the lower and upper quartiles from the curve.

  1. 1Lower quartile at CF 25: ≈ 24 litres
  2. 2Upper quartile at CF 75: ≈ 42 litres
  3. 3IQR ≈ 42 − 24 = 18 litres

Answer16 to 20

Part (b) · 3 marks

Convert $91.00 to litres at $1.75 per litre, then use the graph to find the fraction of customers above this amount.

  1. 1Fuel for $91.00 = 91 ÷ 1.75 = 52 litres
  2. 2Cumulative frequency at 52 litres = 88
  3. 3More than $91: 100 − 88 = 12 customers
  4. 4Fraction = 12/100 = 3/25

Answer12/100 or 6/50 or 3/25

Part (c) · 2 marks

Use the graph to work out the missing frequencies for the intervals 40 < f ≤ 50 up to 70 < f ≤ 80.

  1. 1Read cumulative frequencies: 72 at 40, 86 at 50, 94 at 60, 98 at 70, 100 at 80
  2. 240 < f ≤ 50: 86 − 72 = 14; 50 < f ≤ 60: 94 − 86 = 8
  3. 360 < f ≤ 70: 98 − 94 = 4; 70 < f ≤ 80: 100 − 98 = 2
  4. 4Frequencies: 14, 8, 4, 2

Answer| 40 < f ≤ 50 | 50 < f ≤ 60 | 60 < f ≤ 70 | 70 < f ≤ 80 | | 14 | 8 | 4 | 2 |

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