- Jo wants to find out how much exercise people in her town do. She asks people at the local gym. Give one reason why her sample may be biased.[1]
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A school wants to know how its 1200 students travel in. Asking everyone takes too long, so it asks 60. Whether those 60 answers say anything useful about the whole school depends entirely on how the 60 were chosen. That is the study of sampling.
The big picture
The is everyone or everything you want to know about; a is the part you actually collect data from. A good sample represents the population fairly, so its results can be used to make inferences.
A sample is when some members of the population are more likely to be chosen than others. Random sampling removes that, and larger samples make estimates more reliable — although no sample is ever guaranteed to match the population exactly.
What you'll learn
A collects data from the whole population. It is accurate but can be slow, expensive, or impossible — testing every light bulb until it fails would destroy them all.
A sample is quicker and cheaper, but only gives an estimate.
Tip — When asked for an advantage of a sample, say "quicker" or "cheaper". For a disadvantage, say "may not represent the whole population".
Asking the first 60 students through the gate: late-comers and bus users arriving together may be missed or over-represented.
Asking only Year 7: the sample does not include other year groups.
Surveying people at a gym about exercise habits: they are more active than the general population.
Small samples can also be unrepresentative purely by chance.
In a , every member of the population has an equal chance of being chosen.
Method: number every member of the population, then use a random number generator to pick numbers, ignoring repeats, until the sample is the right size.
A school has 1,200 students, of whom 240 are in Year 7. A stratified sample of 60 students is chosen. How many should be from Year 7?
Random does not mean "whoever is nearby". Asking people you happen to meet is convenient, not random, and it is one of the most common sources of bias.
Scale up sample proportions to estimate population values.
A different sample would give slightly different results, so any estimate carries uncertainty. A larger random sample reduces it.
In a random sample of 50 of the 900 workers at a company, 18 are vegetarian. Estimate how many workers at the company are vegetarian.
Tip — Say "about" or "estimate" — the sample cannot give the exact figure.
Think like an examiner
Remember these
Watch out for these
Stretch yourself
A gym has 450 members: 180 are under 30, 200 are aged 30–59 and 70 are 60 or over. The manager wants a sample of 50 that reflects the age groups. (a) How many from each group should be chosen? (b) In the sample, 12 of the under-30s say they would use a new spin studio. Estimate how many under-30 members in the gym would use it.
Hint — Each group’s share of the sample should match its share of the membership.
Questions students ask
Key takeaways
Exam-style questions
3 original questions · 6 marks, written to match the style and mark allocation of the real papers. Work on paper, then open the mark scheme and tick the marks you earned — method marks count even if the final answer slips.
A company has 400 workers: 120 office staff, 200 factory staff and 80 drivers. A stratified sample of 50 workers is taken.
60 fish in a lake are caught, tagged and released. A week later, 50 fish are caught and 8 of them are tagged.
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