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0580/41 May/Jun 2023, Question 5: Finding the Median and Quartiles

Cambridge IGCSE Mathematics 0580 · Paper 41 (Extended) · Calculator · 13 marks

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The question, in short

Use a cumulative frequency curve for 160 villagers' ages to estimate median, quartiles, a count, a percentile, draw a box plot, and complete a histogram from a frequency table.

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

Part (aia) · 1 mark

Estimate the median age from the cumulative frequency curve.

  1. 1Median at cumulative frequency 160 ÷ 2 = 80
  2. 2Reading across from 80 to the curve and down: median = 25 years

Answer25

Part (aib) · 1 mark

Estimate the lower quartile age from the cumulative frequency curve.

  1. 1Lower quartile at cumulative frequency 160 ÷ 4 = 40
  2. 2Reading across from 40 to the curve and down: LQ ≈ 17.5 years (17 to 18)

Answer17 to 18

Part (aic) · 2 marks

Estimate how many people are aged 50 years or more.

  1. 1At age 50, cumulative frequency = 148
  2. 2Number aged 50 or more = 160 − 148 = 12

Answer12

Part (aid) · 2 marks

Estimate the 65th percentile age from the curve.

  1. 165% of 160 = 0.65 × 160 = 104
  2. 2Reading across from 104 to the curve and down: 65th percentile = 30 years

Answer30

Part (aiia) · 3 marks

Draw a box-and-whisker plot using youngest 1, oldest 70, median 25, quartiles 17.5 and 34.

  1. 1Upper quartile at cumulative frequency 3/4 × 160 = 120, read off as 34
  2. 2Draw whiskers from 1 to 70
  3. 3Draw the box from LQ 17.5 to UQ 34 with the median line at 25

AnswerCorrect box-and-whisker plot: whiskers at 1 and 70, median 25, lower quartile 17 to 18, upper quartile 34

Part (aiib) · 1 mark

Estimate the percentage of villagers younger than the median age.

  1. 1Half the people are younger than the median: 50%

Answer50

Part (b) · 3 marks

Complete the histogram for the given frequency table, using the first block already drawn.

  1. 1Frequency density = frequency ÷ class width
  2. 220 < n ≤ 30: 37 ÷ 10 = 3.7, 30 < n ≤ 50: 24 ÷ 20 = 1.2, 50 < n ≤ 80: 60 ÷ 30 = 2
  3. 3Draw blocks: width 10 (20 to 30) height 3.7, width 20 (30 to 50) height 1.2, width 30 (50 to 80) height 2

AnswerCorrect histogram: blocks of width 10 and height 3.7, width 20 and height 1.2, width 30 and height 2

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Also searched as: 0580/41/M/J/23 · 0580_s23_qp_41 · 0580 s23 41 · question 5.
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