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0580/31 May/Jun 2023, Question 3: Stem-and-Leaf Diagrams

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 8 marks

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The question, in short

Using the 16 listed test scores, complete a stem-and-leaf diagram, find the mode, median and range, finish a grouped bar chart, and work out the percentage scoring 40 or more.

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

Part (a) · 2 marks

Place each of the 16 scores into the correct row of the stem-and-leaf diagram, using the given key.

  1. 1In order: 9, 15, 18, 20, 23, 26, 31, 32, 34, 36, 37, 39, 40, 41, 41, 45
  2. 20 | 9
  3. 31 | 5 8
  4. 42 | 0 3 6
  5. 53 | 1 2 4 6 7 9
  6. 64 | 0 1 1 5

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

Part (b) · 1 mark

Identify the most frequently occurring test score among the 16 values.

  1. 141 appears twice, every other score once
  2. 2Mode = 41

Answer41

Part (c) · 1 mark

Find the median test score of the 16 values.

  1. 116 scores, so the median is halfway between the 8th and 9th
  2. 28th = 32, 9th = 34
  3. 3Median = (32 + 34) ÷ 2 = 33

Answer33

Part (d) · 1 mark

Calculate the range of the test scores.

  1. 1Range = 45 − 9 = 36

Answer36

Part (e) · 2 marks

Complete the grouped bar chart, using the drawn 0 to 9 bar and the 16 scores.

  1. 1Count each row of the stem-and-leaf diagram
  2. 210 to 19: 2, 20 to 29: 3, 30 to 39: 6, 40 to 49: 4
  3. 3Draw bars of heights 2, 3, 6 and 4, same width as the 0 to 9 bar

AnswerCorrect bar chart

Part (f) · 1 mark

Work out the percentage of students whose score is 40 or more.

  1. 1Scores of 40 or more: 40, 41, 41, 45 = 4 students
  2. 24/16 × 100 = 25%

Answer25

Stuck on a step? Read the free lesson: Stem-and-Leaf Diagrams

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Also searched as: 0580/31/M/J/23 · 0580_s23_qp_31 · 0580 s23 31 · question 3.
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