Try each one on paper first, then check a single step. That is worth far more than reading a finished solution.
Example 1 — a stratified sample
A school has 500 students in year 1, 300 in year 2 and 200 in year 3. Take a stratified sample of 100.
- 1Total population: 500+300+200=1000Always compute the total first.
- 2Each stratum contributes in proportion: totalstratum×n
- 3Year 1: 1000500×100=50
- 4Year 2: 1000300×100=30
- 5Year 3: 1000200×100=20
- 6Check: 50+30+20=100 ✓The parts must add to the sample size; rounding may need adjusting so they do.
Example 2 — a systematic sample
Describe how to take a systematic sample of 40 from a numbered list of 800 employees.
- 1k=nN=40800=20The sampling interval.
- 2Choose a random starting number between 1 and 20.The random start is essential — without it the method is not random at all.
- 3Suppose the start is 7.
- 4Take employees 7, 27, 47, 67, … up to 787.Every 20th from the start.
- 5That gives exactly 40 employees.Risk: if the list has a repeating pattern of period 20, the sample is badly skewed.
Example 3 — identifying bias
A researcher surveys shoppers in a city-centre mall on a Tuesday morning about their commute. Identify two sources of bias.
- 1Selection bias: who is in a mall on a Tuesday morning?Not people at work — so the employed are under-represented.
- 2The sampling frame excludes anyone who never visits that mall.Rural residents, those without transport.
- 3Non-response bias: shoppers in a hurry decline.And those in a hurry may well be the ones with the longest commutes.
- 4A larger sample would not fix any of this.It would only estimate the wrong quantity more precisely.
- 5A better design: a random sample from an employee or household register, at varied times.