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0580/32 Feb/Mar 2022, Question 6: Averages from Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 9 marks

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The question, in short

Use a fair 9-sided spinner numbered 2, 3, 5, 5, 5, 6, 6, 7, 8 and a frequency table of 80 dice throws to find probabilities, expected count, mode, range, median and mean.

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

Part (aia) · 1 mark

Find the probability that one spin lands on 8.

  1. 1One 8 out of 9 numbers: P(8) = 1/9

Answer1/9

Part (aib) · 1 mark

Find the probability that one spin gives a number below 7.

  1. 1Numbers less than 7: 2, 3, 5, 5, 5, 6, 6 (7 numbers)
  2. 2P(less than 7) = 7/9

Answer7/9

Part (aii) · 1 mark

Calculate the expected number of times 6 appears in 135 spins.

  1. 1P(6) = 2/9
  2. 2Expected = 135 × 2/9 = 30

Answer30

Part (bi) · 1 mark

State the mode of the 80 dice results.

  1. 1Highest frequency is 16, for the number 2
  2. 2Mode = 2

Answer2

Part (bii) · 1 mark

Find the range of the dice results.

  1. 1Range = 6 − 1 = 5

Answer5

Part (biii) · 1 mark

Find the median of the dice results.

  1. 180 throws: median is between the 40th and 41st values
  2. 2Cumulative frequencies: 15, 31, 45, so both are 3
  3. 3Median = 3

Answer3

Part (biv) · 3 marks

Calculate the mean of the dice results.

  1. 1Σfx = 1×15 + 2×16 + 3×14 + 4×11 + 5×9 + 6×15
  2. 2= 15 + 32 + 42 + 44 + 45 + 90 = 268
  3. 3Mean = 268 ÷ 80 = 3.35

Answer3.35

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