Sheet № 249 · Foundation + Higher · AQA · Edexcel · OCR
Random and Systematic Sampling –
Random and systematic sampling are tested on GCSE Maths papers at Foundation and Higher tier across AQA, Edexcel and OCR. Understanding different sampling methods is essential because the way data is collected affects how reliable the conclusions are. Exam questions ask you to identify sampling methods, describe how to carry them out, and
§Key definitions
Question:
A school has 800 students and wants to survey 40 about school lunches. Describe how to take a simple random sample.
Answer:
Number all 800 students, then use a random number generator to select 40 different numbers. Survey those 40 students. Every student has an equal chance of being chosen.
Advantage:
Easy to carry out on a production line — no need for a full list of items.
Disadvantage:
If there is a regular pattern in production (e.g. every 30th item comes from the same machine), the sample could be biased.
(a)
Year 12: (200 ÷ 600) × 60 = 20 students. Year 13: (400 ÷ 600) × 60 = 40 students.
§Formulas to memorise
Sampling interval = population size ÷ sample size
Number from stratum = (stratum size ÷ population size) × sample size
Ensure each member has an equal chance of selection.
Worked example
A school has 800 students and wants to survey 40 about school lunches. Describe how to take a simple random sample.
Working:
⚠ Common mistakes
- ✗Confusing random with haphazard. "Random" in maths means every member has an equal chance — it does not mean picking whoever is convenient.
- ✗Not calculating the interval for systematic sampling. Always divide population by sample size and show this working.
- ✗Rounding errors in stratified sampling. The numbers from each stratum must be whole numbers and should add up to the total sample size. Round sensibly and adjust if needed.
✦ Exam tips
- →Know the names and definitions of all three methods — random, systematic and stratified.
- →Be ready to describe the process step by step — examiners want method, not just the name.
- →When asked for advantages and disadvantages, give context-specific answers where possible.
- →"Convenience sampling" (e.g. asking friends) is biased — state this if asked to criticise a method.
- →For more on sampling, see sampling methods. For data presentation, see bar charts, pie charts and pictograms.