Sampling Methods (AA SL)
Before you can analyse data, you need a sample that fairly represents the population it's drawn from. This page covers the sampling techniques the exam actually asks you to name, describe and evaluate - simple random, convenience, systematic, quota and stratified - with worked examples and the mistakes that cost marks in "state one advantage" or "identify the flaw" questions. It's part of the broader Sampling & Data Collection topic.
11 questions on this sub-topic.
Working out a sample
Covered under IB syllabus reference SL4.1: concepts of population, sample and random sample, reliability of data sources and bias, interpretation of outliers, and sampling techniques including simple random, convenience, systematic, quota and stratified sampling.
Systematic interval
\(k=\dfrac{\text{population size}}{\text{sample size}}\)
Not in the formula booklet - this is prior knowledge. Pick a random starting point from \(1\) to \(k\), then take every \(k\)th member of the list from there.
Stratified allocation
\(\text{stratum sample} = \text{stratum size} \times \dfrac{\text{sample size}}{\text{population size}}\)
Also not in the booklet. Apply the same sampling fraction to each stratum's own size so the sample stays proportional across all the groups.
Need the full syllabus wording and formula-booklet reference table? See Sampling & Data Collection.
Worked examples
A systematic sample of 50 is taken from a list of 500 people.
State the sampling interval and describe the method.
Worked solution
Interval \(=500/50\) M1
\(=10.\) A1
Choose a random start from the first 10, then take every 10th person. A1
A school has 300 Year 1, 200 Year 2 and 100 Year 3 students (600 total). A stratified sample of 60 is taken.
(a) Find the number of students sampled from each of Year 1, Year 2 and Year 3.
Worked solution
Sampling fraction \(=60/600=\tfrac1{10}.\) M1
Year 1: \(300\times\tfrac1{10}=30\) A1
Year 2: \(200\times\tfrac1{10}=20\) A1
Year 3: \(100\times\tfrac1{10}=10.\) A1
Common mistakes
- Mixing up stratified and quota sampling. Stratified sampling picks members randomly within each proportional subgroup; quota sampling only fixes how many are needed from each group and leaves the interviewer to choose who fills it, so it is not random within a group.
- Applying the sampling fraction to the wrong total. The fraction (sample size divided by population size) must be multiplied by each stratum's own size - not by the overall sample size or population size again.
- Assuming a bigger sample fixes a biased method. A biased technique, such as convenience sampling, stays biased no matter how large it grows; only switching to a properly randomised method removes the bias.
Ready to practise properly?
11 sampling-methods questions, marked instantly like the real exam.
Quick answers
What is the difference between stratified and quota sampling?
Stratified sampling selects members randomly within each proportional subgroup (stratum). Quota sampling only fixes how many are needed from each group and lets the interviewer choose who fills it, so it is not random within a group.
How do you find the sampling interval for systematic sampling?
Divide the population size by the required sample size: \(k = \dfrac{\text{population size}}{\text{sample size}}\). Choose a random starting point between \(1\) and \(k\), then take every \(k\)th member from there. For more on your GDC's role in analysing the resulting data, see the parent topic's GDC guidance.