Sampling Methods (AA HL)
Once you know your population, the next question is how to actually choose who or what gets measured. This page covers the three sampling techniques IB exams test most - simple random, systematic and stratified - along with the calculations each one needs, worked examples, and the mistakes that cost marks. It's part of the broader Sampling & Data Collection topic.
19 questions on this sub-topic.
Sampling methods and their formulas
Covered under IB syllabus reference SL4.1: sampling techniques and their effectiveness, including simple random, convenience, systematic, quota and stratified sampling.
Simple random sampling
Every member of the population has an equal, independent chance of selection - usually via a random-number generator applied to a numbered sampling frame.
Not in the formula booklet - definitionSystematic sampling
\[k = N/n\]
Pick a random start within the first interval, then select every \(k\)th item afterwards.
Not in the formula booklet - definitionStratified sampling
\(\text{stratum sample size} = \dfrac{\text{stratum size}}{\text{population size}}\times n\)
Split the population into subgroups (strata) first, then sample proportionally from each so every subgroup is represented fairly.
Not in the formula booklet - proportional reasoningNeed the full syllabus wording and reliability/bias notes? 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. How many from each year?
(a) State the number from Year 1.
(b) State the number from Year 2.
(c) State the number from Year 3.
Worked solution
Sampling fraction \(=60/600=\tfrac1{10}.\) M1
Year 1: 30, A1 Year 2: 20, A1 Year 3: 10. A1
Common mistakes
- Mixing up systematic and stratified sampling. Systematic sampling picks every \(k\)th item from one list; stratified sampling splits the population into subgroups first and samples proportionally from each - they're testing different things and aren't interchangeable answers.
- Forgetting that a sample can be biased even with perfect randomness. If the sampling frame itself excludes part of the population (like a directory missing unlisted numbers), no amount of careful random selection afterwards fixes that.
- Rounding stratum sizes independently. When \(\dfrac{\text{stratum size}}{\text{population size}}\times n\) doesn't give a whole number, rounding each stratum separately can make the parts add up to more or less than the intended total sample size - check the sum matches \(n\) before giving a final answer.
Ready to practise properly?
19 sampling-methods questions, marked instantly like the real exam.
Quick answers
How do you find the sampling interval for systematic sampling?
Divide the population size \(N\) by the sample size \(n\) to get \(k = N/n\), the sampling interval. Choose a random starting point within the first interval, then select every \(k\)th item after that.
How do you work out a stratified sample size?
Multiply the overall sample size \(n\) by the fraction each stratum makes up of the total population: \(\text{stratum sample size} = \dfrac{\text{stratum size}}{\text{population size}}\times n\).