Sheet № 73 · Foundation + Higher · AQA · Edexcel · OCR
Sampling Methods –
Sampling methods is a topic that bridges Foundation and Higher GCSE Maths and appears across AQA, Edexcel and OCR exam papers. In real life, it is rarely possible to survey every member of a population, so you take a sample instead. The way you choose that sample matters — a biased sample gives misleading results, while a well-chosen samp
§Key definitions
Advantages:
Eliminates selection bias; every member has an equal chance.
Disadvantages:
Needs a complete list of the population (a sampling frame); may not represent subgroups proportionally by chance, especially with small samples.
Question:
A school has 600 pupils and wants to survey a sample of 60. The table shows the number of pupils in each year group.
(a)
Sample fraction = 40/250 = 4/25.
(b)
Stratified sampling ensures each department is represented in proportion to its size. Random sampling might, by chance, over-represent one department and under-represent another, especially in a sample of only 40.
§Formulas to memorise
k = Population size ÷ Sample size
Number from stratum = (Stratum size ÷ Population size) × Sample size
Round to the nearest whole number if necessary (check the total still equals the sample size).
Sample fraction = 60/600 = 1/10.
Worked example
A school has 600 pupils and wants to survey a sample of 60. The table shows the number of pupils in each year group. | Year | 7 | 8 | 9 | 10 | 11 | |---|---|---|---|---|---| | Pupils | 140 | 130 | 120 | 110 | 100 | Using stratified sampling
Working:
⚠ Common mistakes
- ✗Confusing sample and population — the population is everyone; the sample is the subset you actually survey.
- ✗Forgetting to round stratified sampling numbers — you cannot sample 12.8 people. Round sensibly and check the total still matches.
- ✗Applying the wrong formula — for stratified sampling, use (stratum ÷ total) × sample size. Do not divide the sample size equally across strata.
- ✗Not explaining bias clearly — saying a sample "might not be fair" is vague. Explain which groups could be over- or under-represented and why.
- ✗Thinking random = haphazard — random sampling requires a systematic method (e.g. random number generator), not just picking people casually.
✦ Exam tips
- →Know the three main types — random, systematic and stratified. Be ready to describe each and give an advantage and disadvantage.
- →Stratified sampling calculations are very common — learn the formula and practise with different strata sizes. This is straightforward arithmetic that earns guaranteed marks.
- →Bias questions require specific explanations — always say which group is over- or under-represented and link it to the sampling method used.
- →Large samples are more reliable — if asked how to improve a survey, suggest increasing the sample size. This reduces the effect of random variation.
- →Link to data representation — once data is collected, you will likely need to display it using charts or calculate averages. See frequency tables and grouped data and bar charts, pie charts and pictograms.