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0580/31 May/Jun 2024, Question 4: Expressing One Quantity as a Percentage

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 11 marks

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The question, in short

Using a stem-and-leaf diagram of 16 workers' ages on 1st January 2022, find range, mode, median, a percentage, later-year statistics, update the diagram for 2024, and find the owner's age x.

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

Part (ai) · 1 mark

Work out the range of the ages from the stem-and-leaf diagram.

  1. 1Range = 61 − 23 = 38

Answer38

Part (aii) · 1 mark

Write down the mode of the ages.

  1. 136 appears three times: mode = 36

Answer36

Part (aiii) · 1 mark

Work out the median age.

  1. 116 values: median is between the 8th and 9th, 39 and 41
  2. 2Median = (39 + 41) ÷ 2 = 40

Answer40

Part (aiv) · 2 marks

Work out the percentage of workers older than 40 but younger than 60.

  1. 1Older than 40 and younger than 60: 41, 41, 47, 50, 57, 57, 58 = 7 workers
  2. 27/16 × 100 = 43.75%

Answer43.75

Part (b) · 2 marks

On 1st January 2023, with the same 16 workers, write down the range, mode and median.

  1. 1A year later every worker is 1 year older, so every age goes up by 1.
  2. 2Range does not change: 61 − 23 = 38
  3. 3Mode was 36 (it appears three times), so now 37.
  4. 4Median was the mean of the 8th and 9th ages: (39 + 41) ÷ 2 = 40, so now 41.
  5. 5Range 38, Mode 37, Median 41

AnswerRange 38, Mode 37, Median 41

Part (c) · 2 marks

Complete the 2024 stem-and-leaf diagram after the oldest worker leaves and a replacement born 12th November 1970 joins.

  1. 12024 ages are 2022 ages + 2: 25 27 29 36 38 38 38 41 43 43 49 52 59 59 60 63
  2. 2The oldest (63) leaves; the new worker is 53 on 1 January 2024 (birthday 12 November 1970)
  3. 34 | 1 3 3 9
  4. 45 | 2 3 9 9
  5. 56 | 0

Answer| 2 | 5 7 9 | | 3 | 6 8 8 8 | | 4 | 1 3 3 9 | | 5 | 2 3 9 9 | | 6 | 0 |

Part (d) · 2 marks

Find prime x where x + 2 is square and x − 2 is a multiple of 9.

  1. 1x + 2 is a square: try 49 → x = 47
  2. 247 is prime and 47 − 2 = 45 = 5 × 9
  3. 3x = 47

Answer47

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Also searched as: 0580/31/M/J/24 · 0580_s24_qp_31 · 0580 s24 31 · question 4.
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