How to teach sampling methods
Year 8 to Year 9 (ages 13 to 15)
Since studying an entire population is often too costly or slow, statisticians study a sample instead. This unit covers the different ways a sample can be chosen, how sample size affects reliability, and why a poorly chosen sample can mislead.
How to teach it
- Contrast a census (everyone) with a sample (a subset), discussing when each is practical.
- Introduce random, systematic and convenience sampling, with a real example of each and a discussion of who might be missed.
- Explain representativeness: a good sample reflects the population's key characteristics, not just whoever was easy to ask.
- Compare a small sample with a larger one on the same question, showing how a bigger sample usually reduces chance variation.
- Critique a real or invented survey (e.g. an online poll) for sampling bias, identifying who was excluded and why it matters.
Common mistakes
- Assuming any sample is automatically representative just because it is large.
- Confusing a convenience sample (easiest to reach) with a random sample (equal chance for everyone).
- Believing a sample must include a fixed percentage of the population to be reliable, rather than being about HOW it was chosen.
- Overlooking who a sampling method excludes (e.g. a phone survey during work hours misses people at their jobs).
Frequently asked questions
What is the difference between a census and a sample?
A census collects data from every member of a population; a sample collects data from only a subset. Samples are usually faster and cheaper, but must be chosen carefully to represent the whole population fairly.
What makes a sample 'representative'?
A representative sample reflects the key characteristics of the whole population it is drawn from. A random sample, where every member has an equal chance of being chosen, is one reliable way to achieve this.
Why is a convenience sample often biased?
A convenience sample only includes whoever is easiest to reach, which can over-represent some groups and under-represent others, so its results may not generalise to the whole population.
What year is sampling taught?
In the Australian Curriculum, data collection methods and sampling from sources are Year 8 skills (AC9M8ST01-03), with analysing how sampling and display choices can shape survey results continuing at Year 9 (AC9M9ST02).
Practise with free worksheets
Printable worksheets with answer keys that are never wrong.