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Welcome to GCSE Edexcel Maths revision.

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Topic M 39: Sampling and interpreting data.

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This video covers Higher tier.

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It includes the shared content and the labelled Higher extensions.

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A population is the complete group being studied.

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A sample is a smaller group selected to investigate it.

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A census measures every member, which can be costly or impractical.

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Discrete numerical data are counted, such as numbers of siblings.

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Continuous numerical data are measured, such as height.

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Categorical data describe groups, such as a travel method.

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A sample should represent the population relevant to the question.

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Asking only one friendship group about a whole school's preferences risks bias.

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Random sampling gives each population member an equal chance in a simple random selection.

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Use a complete sampling frame and random numbers; avoid duplicate selections if sampling without replacement.

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Systematic sampling takes every kth member after a random start.

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Check that a repeating pattern in the list does not bias the chosen sample.

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Questionnaires should use clear wording and non-overlapping response categories that cover possible answers.

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Avoid leading questions such as Don't you agree that and so on?.

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A larger representative sample usually reduces random sampling variation, but size alone cannot remove selection bias.

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Ten thousand volunteers may still be unrepresentative.

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Non-response can bias results if people who respond differ from those who do not.

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State the population, sample size, method and missing responses when interpreting a survey.

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Use statistics to describe distributions rather than claiming every individual has the average value.

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A mean of 2.4 siblings is possible even though no one has 2.4 siblings.

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Compare both a measure of centre and spread, with context.

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A higher mean journey time and larger range suggest longer journeys on average and more variation.

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Stratified sampling separates a population into groups, then samples in proportion to each group's size.

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Randomly select within each group to avoid bias.

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A proportional stratified sample

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Worked example: A school has 120 Year 10 and 180 Year 11 students.

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For a proportional sample of 50, choose 50 multiplied by 120 over 300 equals 20 from Year 10 and 30 from Year 11.

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For non-integer group allocations, round carefully so the sample total still matches the target.

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Explain how any remaining places are assigned.

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Stratification improves representation of the chosen groups; it does not guarantee every relevant characteristic is represented or that answers are unbiased.

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That completes Sampling and interpreting data.

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Revisit the notes and test yourself on the revision website.