Key Idea: This topic is about choosing a fair sample and judging how trustworthy it is. Exam parts ask you to name the sampling method, do a quick calculation, or explain why a sample is biased — all non-calculator (Paper 1).
👥 Population, sample & why we sample
Important: A sample is reliable only when it represents the whole population. A biased sample over- or under-represents part of it. A bigger sample helps — but a large unfair sample is still biased.
🎯 The five sampling techniques
- population size
- sample size
- systematic interval — take every k-th member
- population size
- total sample size
✏️ IB-style worked examples
IB-style question — systematic sampling interval
A gym has 900 members. A sample of 60 is taken systematically. Find the sampling interval and describe how to choose the sample.
Step by step:
Interval = population ÷ sample size.
Random start, then step by k.
Final answer:
k = 15: pick a random start from the first 15, then take every 15th member.
IB-style question — stratified sample size
A college has 700 day students and 300 evening students (1000 total). A stratified sample of 50 is taken. Find how many day students should be in the sample.
Step by step:
Group proportion × sample size.
Evaluate.
Final answer:
35 day students (and so 15 evening students — they total 50).
Important: For systematic sampling the interval is k = N ÷ n, not n itself. With 900 members and a sample of 60, k = 15, not 60. And always check stratified shares sum to n.
Tap each card to reveal the answer.
Exam Tips
- Name the population as the WHOLE group the question is about, not just those measured.
- For 'why sample?': say cheaper, faster, or the test destroys the item.
- Systematic interval is k = N ÷ n; stratified share = (group ÷ N) × n — check shares total n.
- Quota and convenience are the usual answers when asked which method is biased.
- For 'why unreliable?': name the group that is over- or under-represented.