Sampling Methods (AI SL)
Once you know what a population and a sample are, the next skill is choosing - and correctly applying - a sampling technique. This page covers simple random, systematic and stratified sampling, the two calculations that come up most in exam questions, and the wording that separates each method from the others. It's part of the broader Sampling & Data Collection topic.
24 questions on this sub-topic.
Choosing a sampling method
Covered under IB syllabus reference SL4.1, which also lists convenience and quota sampling as effectiveness comparisons - but simple random, systematic and stratified are the three you'll actually have to calculate.
Simple random sampling
Number every member of the population, then use technology to generate random numbers and pick the sample - every individual and every combination has an equal chance of selection.
Not in the formula booklet - selection procedureSystematic sampling
\(\text{Sampling interval} = \dfrac{\text{population size}}{\text{sample size}}\)
Choose a random starting point within the first interval, then take every member at that interval after it.
Not in booklet - direct proportionStratified sampling
\(\text{Stratum sample size} = \dfrac{\text{sample size}}{\text{population size}}\times\) stratum size
Split the population into strata, then apply the same sampling fraction to each one so every group is represented proportionally.
Not in booklet - direct proportionNeed the reliability, bias and outlier definitions that go with this? See Data types and collection, or the full Sampling & Data Collection page for GDC guidance.
Worked examples
A systematic sample of 50 is taken from a list of 500 people.
(a)(i) State the sampling interval.
(a)(ii) Describe the method.
Worked solution
(a)(i) Interval \(=500/50\) M1
\(=10.\) A1
(a)(ii) Choose a random start from the first 10, then take every 10th person. A1
A company has \(300\) staff: \(150\) office, \(90\) factory, \(60\) sales. A stratified sample of \(20\) is taken.
(a) Find the number from office.
(b) Find the number from factory.
(c) Find the number from sales.
Worked solution
(a) Office \(10.\) M1
\(10.\) A1
(b) Factory \(6.\) A1
(c) Sales \(4.\) A1
Common mistakes
- Mixing up systematic and random. Systematic sampling still needs a genuine random starting point inside the first interval - always taking position 1 as the start makes it a fixed, non-random rule.
- Not rounding stratified sample sizes sensibly. Stratified calculations often produce a decimal - round to the nearest whole number and check your rounded group sizes still add up to the total sample size.
- Calling convenience sampling "random". Choosing whoever is easiest to reach - people leaving a particular shop, say - is convenience sampling, not simple random sampling, even when the selection feels arbitrary.
Ready to practise properly?
24 sampling-methods questions, marked instantly like the real exam.
Quick answers
What is the formula for a systematic sampling interval?
\(\text{Sampling interval} = \dfrac{\text{population size}}{\text{sample size}}\). Pick a random start within the first interval, then take every \(k\)th member after that.
How do you find a stratified sample size for each group?
\(\text{Stratum sample size} = \dfrac{\text{sample size}}{\text{population size}}\times\) stratum size - the same sampling fraction applied to every group so each is represented proportionally.