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Statistics & Probability · Foundation & Higher

Sampling & bias

Sampling is choosing a group to represent a population. A biased sample does not fairly represent the population, which makes conclusions unreliable.

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Key facts to remember

  • 1A random sample gives every member of the population an equal chance of being selected.
  • 2A biased sample over- or under-represents certain groups.
  • 3Larger samples give more reliable results.
  • 4Stratified sampling selects from each subgroup in proportion to its size.
  • 5Common sources of bias: asking leading questions, sampling only convenient groups, timing of survey.
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Formulas

Stratified sample
Sample size from group = (group size / population) × total sample size
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Worked examples

Example 1

A school has 400 Year 10 and 600 Year 11 students. A stratified sample of 50 is taken. How many should be from Year 10?

Working

  1. Year 10 proportion = 400/1000 = 2/5
  2. Year 10 in sample = (2/5) × 50 = 20
Answer20 students from Year 10
Example 2

A survey asks "Don't you agree our school canteen food is terrible?" Identify the bias.

Working

  1. The question is leading — it suggests a negative view
  2. Respondents are more likely to agree due to the phrasing
  3. This introduces response bias
AnswerThe question is biased as it leads respondents towards a negative answer.
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Common mistakes

✗Confusing a large sample with an unbiased sample — a large biased sample is still biased.
✗Not rounding stratified sample sizes to whole numbers.
✗Failing to identify how a question or method introduces bias.
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Exam tips

✓For bias questions, explain specifically how the method excludes certain groups or influences responses.
✓For stratified sampling, always calculate the proportion first, then multiply by the total sample size.

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