Sampling and inference

Edexcel typically tests this through worded scenarios where students must (a) state the population, (b) suggest a representative sampling method, and (c) explain why a proposed sample might be biased.

Population vs sample

The population is the full group you want information about (e.g. "all Year 11 students at a UK school"). A sample is a smaller subset chosen to represent the population.

We sample because surveying the whole population is usually impractical or expensive.

Random sampling

Every member of the population has an equal chance of being selected. Methods include:

• Numbering all members and using a random number generator.
• Drawing names from a hat (small populations).

Stratified sampling (Higher only)

Population is divided into strata (subgroups, e.g. by year group or gender). Sample size in each stratum is proportional to the stratum's share of the population.

If a school has 200 Y9, 180 Y10, 220 Y11 students (total 600) and we want a sample of 60:

• Y9: 60 × 200/600 = 20.
• Y10: 60 × 180/600 = 18.
• Y11: 60 × 220/600 = 22. Total = 60 ✓.

Common biased samples (Edexcel exam staple)

1. Convenience samples — only friends, only first 30 to enter a building, etc.
2. Self-selected samples — online polls where only motivated people respond.
3. Sampling at the wrong location/time — surveying about train use only on a station platform.
4. Insufficient size — a sample of 5 cannot represent 600.

Inferring properties of a population

If a sample shows 40 out of 100 prefer brand A, an estimate for the population proportion is 40% (= 0.4). For a population of 5000, expect approximately 5000 × 0.4 = 2000 to prefer brand A.

Edexcel exam tip

When asked "give one reason why this sample may be biased", give a specific reason linked to the scenario — not generic. "Only asked her friends" earns the mark; "the sample is too small" rarely does.

Common Edexcel question pattern

"Sara wants to find out how often Year 11 students at her school revise. She asks 10 of her friends. Give two reasons why this is not a good sample." (2 marks)

Acceptable answers (Edexcel mark-scheme style):

• "Only her friends" (her friends may share habits / not representative).
• "Sample size too small" or "10 is not enough".
• "Only Year 11 — but the question already restricts to Year 11" → wrong, would be marked zero.