Why sample?
Studying an entire population is often too expensive, slow or impossible. A sample is a smaller group that we hope represents the whole. How you choose it, the sampling method, decides whether the results can be trusted.
Probability sampling methods
These use randomness, which helps avoid bias.
| Method | How it works | Example |
|---|---|---|
| Simple random sample | every member has an equal chance | draw 50 student numbers from a computer generator |
| Systematic sample | random start, then every kth person | every 10th customer through the door |
| Stratified sample | split into groups (strata), randomly sample each in proportion | sample each grade level according to its size |
| Cluster sample | randomly pick whole groups, survey everyone in them | randomly choose 5 classrooms and survey all students in them |
| Multi-stage | combine methods in stages | pick provinces, then cities, then households |
Non-probability methods
| Method | How | Problem |
|---|---|---|
| Convenience sample | survey whoever is handy | not representative |
| Voluntary response | people choose to respond | strong opinions over-represented |
| Judgment sample | researcher picks "typical" people | researcher’s bias |
Example: An online poll on a sports website about funding for arenas will mostly reach sports fans, so it won’t represent all citizens.
Stratified example
A school has 600 Grade 9s, 500 Grade 10s, 450 Grade 11s and 450 Grade 12s (2,000 total). A 100-student stratified sample:
| Grade | Share | Sample |
|---|---|---|
| 9 | 30% | 30 |
| 10 | 25% | 25 |
| 11 | 22.5% | 22 or 23 |
| 12 | 22.5% | 22 or 23 |
Systematic example
1,200 names on a list; you want 60. k = 1,200 ÷ 60 = 20. Pick a random start from 1–20 (say 7), then 7, 27, 47, …
Caution: if the list has a repeating pattern every 20 names, this method could be biased.
Sample size
Larger samples usually give more reliable results, but a large biased sample is still biased. A well-chosen random sample of 1,000 can represent millions.
Choosing a method
- Population list available, fairly uniform? → simple random.
- Important subgroups? → stratified.
- Spread out geographically? → cluster.
- Steady stream of people? → systematic.
Worked examples
Example 1: Surveying every 5th shopper leaving a mall. Method? Systematic.
Example 2: Randomly choosing 4 of 20 sports teams and surveying all players. Method? Cluster.
Example 3: Asking your friends about a new school policy. Method and problem? Convenience; likely unrepresentative.
Common mistakes
- Equating "random" with "haphazard". True randomness needs a chance process.
- Assuming a big sample fixes a biased method.
- Ignoring subgroups that matter.
Try it yourself
- Name the method: names drawn from a hat.
- Name the method: survey 10% of each department in a company.
- Why is a TV call-in poll unreliable?
- 900 students; you want a systematic sample of 45. What is k?
Answers: 1) simple random 2) stratified 3) It’s voluntary response; people with strong opinions are more likely to call. 4) 20
Quick recap
- A good sampling method gives a representative sample.
- Probability methods: simple random sample, systematic sample, stratified sample, cluster sample.
- Convenience samples and voluntary responses are prone to bias.