S1.2StatisticsCore

Sampling

Random sampling gives every unit a known chance of selection, which keeps the sample fair. There are three methods you must know: simple random, systematic and stratified — each with its own pros and cons.

25 min Data Collection

Edexcel AS Level Maths: Data Collection (Part 1) — Random SamplingCurated by Kepler, not produced by us. Watch it before the notes below.

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What you'll be able to do

Describe simple random sampling
Describe systematic sampling
Describe stratified sampling
Compare the methods and their limitations

Simple random sampling

Every member of the population has an $\textbf{equal}$ chance of being chosen — for example by numbering the sampling frame and using a random number generator. It is fair and bias-free but needs a complete list of the population.

Systematic sampling

Choose units at $\textbf{regular intervals}$ through an ordered list — every $k$ th item after a random start. If the population is $N$ and the sample size $n$ , the interval is $k = \dfrac{N}{n}$ .

k = \dfrac{N}{n}

Sample every

k

th unit after a random starting point.

Example 1Choose a systematic sample of 50 from 1000 people. What is the interval?

k = \dfrac{1000}{50}

Answerevery 20th person

Stratified sampling

Split the population into $\textbf{groups (strata)}$ , then sample from each group in proportion to its size. This makes the sample representative of every subgroup.

\text{number from a stratum} = \dfrac{\text{stratum size}}{\text{population}} \times n

Sample each group in proportion to its size.

Example 1A school has 600 girls and 400 boys. For a stratified sample of 50, how many girls?

\dfrac{600}{1000} \times 50

Answer30 girls

Tip — Stratified: each group’s share of the sample matches its share of the population.

Formula recap

k = \dfrac{N}{n}

Systematic sampling interval.

\dfrac{\text{stratum}}{N} \times n

Stratified sample per group.

\text{simple random: equal chance for all}

Simple random sampling.

Common mistakes to avoid

Calling any small selection a “random sample”.

Random sampling requires a known, fair chance of selection for each unit.

Rounding stratified numbers so the total no longer equals n.

Make sure the group sizes add back up to the required sample size.

Key takeaways

Simple random: equal chance for everyone (needs a full list).
Systematic: every kth unit (k = N/n) after a random start.
Stratified: sample each group in proportion to its size.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

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Related lessons

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Put the methods into practice: see how A-Level maths duels work. An account is required to play; the overview and sample are public.