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4024/21 May/Jun 2021, Question 2: Averages from Frequency Tables

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 9 marks

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The question, in short

From a bar chart of household sizes for 50 houses, find the mode, median and mean, then work out probabilities for houses chosen at random.

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

Part (a) · 1 mark

Identify the number of people per house that occurs most often from the bar chart.

  1. 1Highest bar is 4 people (frequency 12)
  2. 2Mode = 4

Answer4

Part (b) · 1 mark

Find the median number of people per house for the 50 houses.

  1. 1Median is the 25th/26th value
  2. 2Cumulative: 7, 18, 28, … so both are 3
  3. 3Median = 3

Answer3

Part (c) · 3 marks

Calculate the mean number of people per house using the chart frequencies.

  1. 1Total = 7 × 1 + 11 × 2 + 10 × 3 + 12 × 4 + 6 × 5 + 4 × 6 = 161
  2. 2Mean = 161 ÷ 50 = 3.22

Answer3.22 or 3 11/50

Part (d) · 1 mark

Find the probability that a randomly chosen house has exactly 3 people.

  1. 1P(3 people) = 10/50

Answer10/50

Part (e) · 3 marks

For two houses chosen at random, find the probability exactly one has 5 people.

  1. 1P(one has 5, other not) = 6/50 × 44/49 × 2
  2. 2= 528/2450
  3. 3= 264/1225

Answer264/1225

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