What is important to know about Sampling & bias?

A random sample gives every member of the population an equal chance of being selected.

A biased sample over- or under-represents certain groups.

Larger samples give more reliable results.

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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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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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Stratified sample

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

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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?

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Answer20 students from Year 10

Example 2

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

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AnswerThe question is biased as it leads respondents towards a negative answer.

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✗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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✓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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