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
| Term | What it means |
|---|---|
| Population | Every individual the study is about (the whole group). |
| Sample | The smaller part you actually measure. |
| Census | Data from the whole population. |
| Why sample? | It's cheaper, faster, or the test is destructive (quote one for a 'give a reason' part). |
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
| Technique | How it works | Main drawback |
|---|---|---|
| Simple random | Every member is equally likely (draw lots / random numbers). | Needs a full list; can miss small groups by chance. |
| Systematic | Order the list, random start, then take every k-th member. | Biased if the list has a hidden pattern matching k. |
| Stratified | Split into groups, sample each in proportion to its size. | You must know each group's size in advance. |
| Quota | Fill fixed numbers per group, but pick members non-randomly. | Selection isn't random → easily biased. |
| Convenience | Take whoever is easiest / first available. | Usually unrepresentative → most biased of all. |
- 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.
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.
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.
What is the population in a study? The whole group the study is about — not just those measured.
Give one reason to sample instead of a census It's cheaper, faster, or the test is destructive (any one).
Systematic interval for N = 800, n = 50 k = 16 — that's 800 ÷ 50.
Stratified share of a 60-strong group when N = 1000, n = 50 3 — (60 ÷ 1000) × 50 = 3.
Which two methods are most likely biased? Quota and convenience — selection isn't random.
Why isn't a huge sample automatically reliable? A large unfair sample is still biased — it must also be representative.
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.