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0580/32 May/Jun 2023, Question 2: Bar Charts and Composite Bar Charts

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 12 marks

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The question, in short

Use a partly filled frequency table and bar chart for 61 words, plus a second table and a list of word lengths, to complete totals, find averages, a probability and spread.

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

Part (ai) · 3 marks

Use the 61-word total and the bar chart to fill the missing frequencies for 2 and 5 letters, then complete the table and chart.

  1. 1From the bar chart, 3 letters has frequency 14
  2. 2Missing total: 61 − (7 + 12 + 14 + 15 + 5) = 8, so 5 letters has frequency 8
  3. 3Draw bars of height 12 at 2 letters and 8 at 5 letters

Answer| Number of letters | 3 | 5 | | Frequency | 14 | 8 | Bars with heights 12 (2 letters) and 8 (5 letters)

Part (aii) · 1 mark

State the most common number of letters from the completed frequencies.

  1. 1Highest frequency is 15, for 4 letters
  2. 2Mode = 4

Answer4

Part (bi) · 3 marks

Calculate the mean number of letters from the second frequency table.

  1. 1Total letters = 1×10 + 2×18 + 3×9 + 4×6 + 5×5 + 6×2 = 134
  2. 2Number of words = 10 + 18 + 9 + 6 + 5 + 2 = 50
  3. 3Mean = 134 ÷ 50 = 2.68

Answer2.68

Part (bii) · 2 marks

Find the probability that a randomly chosen word has more than three letters.

  1. 1More than three letters: 6 + 5 + 2 = 13 words
  2. 2P = 13/50

Answer13/50

Part (ci) · 2 marks

Find the median of the twelve listed word lengths.

  1. 1In order: 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 9
  2. 212 values: median is between the 6th (3) and 7th (4)
  3. 3Median = (3 + 4) ÷ 2 = 3.5

Answer3.5

Part (cii) · 1 mark

Find the range of the listed word lengths.

  1. 1Range = 9 − 1 = 8

Answer8

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Also searched as: 0580/32/M/J/23 · 0580_s23_qp_32 · 0580 s23 32 · question 2.
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