K: Statistical sampling — AQA A-Level Mathematics
Test yourself on K: Statistical sampling with AQA A-Level practice questions.
7 days Premium · Then free forever · No card, no charge
K: Statistical sampling explained
A population is the entire group you want to study; a sample is a subset selected from it.
Read the full explanation
Because measuring every member is often impractical, you use a sample to make informal inferences about the population. Simple random sampling gives every member an equal chance of selection, often via random numbers. Opportunity sampling uses whoever is available, which is quick but biased. When solving a statistical problem, you must choose or critique a technique, recognising that different samples can produce different conclusions. For example, sampling 30 students from a school to estimate average daily screen time: a random sample may over- or under-represent heavy users, while an opportunity sample outside the library may over-represent studious students. Always link the method to the context and acknowledge variability.
Your focus
- Define population and sample correctly and distinguish between them in a given context.
- Carry out or describe a simple random sampling procedure and explain why it is random.
- Evaluate an opportunity sample and explain how it may lead to biased conclusions.
Show all 4 objectives
- Explain why two different samples from the same population may produce different conclusions.
K: Statistical sampling exam tips
Marking Points
- Defines population as the whole set of individuals or items of interest and sample as a subset drawn from that population.
- Explains that a sample is used to make informal inferences about the population, acknowledging that sample results are estimates rather than exact population values.
- Describes simple random sampling accurately, including the requirement that every member of the population has an equal chance of being selected, and a valid selection method such as random number generation or lottery.
- Describes opportunity sampling as selecting individuals who are conveniently available at the time, and identifies this as a potential source of bias.
- Critiques or selects a sampling technique by relating its practical advantages and disadvantages to the specific statistical problem, such as cost, time, accessibility and representativeness.
- Explains that different samples from the same population can lead to different conclusions, and that this variability is expected and should be considered when interpreting results.
Examiner Tips
- 💡When asked to critique a sampling method, always refer to the specific context: state who or what is in the population, how the sample was selected, and why that might bias the results.
- 💡Use precise language: say 'every member of the population has an equal chance of being selected' for simple random sampling, and 'selected because they are easily available' for opportunity sampling.
- 💡If a question asks whether different samples could lead to different conclusions, answer yes and explain that natural variation between samples means estimates may differ; do not claim that one sample is necessarily wrong.
Common Mistakes
- Confusing population with sample: for example, calling the 50 people surveyed the population. Correction: the population is the entire group about which conclusions are drawn; the 50 people form the sample.
- Believing that a simple random sample is always perfectly representative. Correction: random sampling reduces bias but still produces sample-to-sample variation; different random samples can give different estimates.
- Treating opportunity sampling as equivalent to random sampling. Correction: opportunity sampling selects whoever is available, so it often over-represents certain groups and cannot support the same strength of inference as a random sample.