What population and sample mean
Big idea: Population means the full group you want conclusions about.
Sample means the smaller group you actually collect data from.
Example: if you study IB Mathematics students worldwide, that full group is the population.
If you collect data from 600 IB students from selected schools, that 600 is your sample.
- Population
- The entire target group.
- Sample
- A subset chosen from that target group.
- Sampling
- How the subset is selected.
Fast check: Ask: is this ALL students/items, or only SOME?
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How to choose a sample
Goal: A good sample should represent the population fairly.
It should reduce bias.
| Method | How it works | When useful |
|---|---|---|
| Simple random | Each member has equal chance | General surveys |
| Stratified | Split into groups, sample each group | When subgroups differ |
| Systematic | Pick every k-th item | Ordered lists |
Worked example
School has 1200 students.
You need a sample of 120 using systematic sampling.
Step by step
- Find interval: 1200/120 = 10
- Pick random start from 1 to 10
- Then select every 10th student
Final answer
Systematic sample interval is 10.
IB language: Write why your method is fair, not only what method you used.
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Bias, sample size, and reliability
Bias: Bias means your method pushes results in one direction.
Biased samples give unfair conclusions.
Common mistakes
- Only surveying one friend group
- Surveying only one school type
- Using voluntary responses only
Better choices
- Use random or stratified selection
- Include different subgroups
- Set minimum sample size
Larger samples usually reduce random error, but large biased samples are still poor.
Exam trap: Do not claim a sample is reliable unless you justify method and representation.
Past-paper style question patterns
What IB asks: IB often asks you to identify population, describe a sampling method, and comment on bias/reliability.
Worked example
A researcher studies daily screen time of teenagers in a city.
She surveys 80 students from one private school.
(a) State population and sample.
(b) Suggest one improvement.
Answer plan
- Population: all teenagers in that city
- Sample: 80 students from one private school
- Issue: sample is not representative
- Improvement: use stratified sample across multiple schools
Final answer
Strong answer defines both terms and explains representativeness.
Exam tips
- Define population and sample in context.
- Name the bias source clearly.
- Give one realistic improvement.