Population and samples — Edexcel A-Level Statistics
Test yourself on Population and samples with PEARSON EDEXCEL A-Level practice questions.
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Population and samples explained
A random sample is selected so that every member of the population has a known chance of selection.
Read the full explanation
In a simple random sample, items are chosen without replacement: once selected, an item cannot be chosen again, so the sample contains distinct members and the population size effectively reduces after each draw. In an unrestricted random sample, items are chosen with replacement: each selection is made from the full population, so the same item may appear more than once and the probabilities stay constant across draws. For example, drawing two names from a hat and not returning the first name gives a simple random sample; returning the first name before the second draw gives an unrestricted random sample. Recognising which sampling method applies determines whether probabilities change between draws.
Your focus
- Define a simple random sample as sampling without replacement.
- Define an unrestricted random sample as sampling with replacement.
- Explain how replacement affects the probabilities of successive selections.
Population and samples exam tips
Marking Points
- Defines a simple random sample as sampling without replacement, where selected items are not returned to the population.
- Defines an unrestricted random sample as sampling with replacement, where each item is returned before the next draw.
- States that in simple random sampling the probabilities change between draws as the population size decreases.
- States that in unrestricted random sampling the probabilities remain constant because the population is unchanged.
- Identifies from a described procedure whether sampling is with or without replacement.
- Recognises that an unrestricted sample may contain repeated items while a simple random sample cannot.
Examiner Tips
- 💡Look for the phrase 'returned to the population' to identify unrestricted sampling.
- 💡If the population size decreases after each selection, the sample is simple (without replacement).
- 💡Check whether repeated items are possible; if so, the sampling is with replacement.
- 💡Link the sampling method to whether probabilities are constant or changing across draws.
Common Mistakes
- Treating 'simple' and 'unrestricted' as interchangeable. Correction: simple means without replacement, unrestricted means with replacement.
- Assuming probabilities stay the same in a simple random sample. Correction: without replacement, the denominator decreases after each draw, so probabilities change.
- Believing an unrestricted sample cannot contain duplicates. Correction: with replacement, the same item can be selected more than once.
- Confusing random sampling with quota or convenience sampling. Correction: random sampling requires every population member to have a known chance of selection.