Understand the idea.
Start with the population
The population is the full group your question concerns; the sample is the group actually measured. Define the population precisely, then check the sampling frame: the list or access method used to reach possible participants. An incomplete frame can exclude important voices.
Random sampling uses chance to choose from a suitable frame. Systematic sampling uses a random start and a fixed interval. Stratified sampling separates relevant groups, then samples within each. These methods support fair selection but do not guarantee a perfectly representative result.
Look for missing voices
A convenience sample reaches whoever is easiest to find, while a voluntary poll includes whoever chooses to respond. Explain which groups may be over-represented or absent and why that matters for this particular question. A large biased sample still has this weakness.
Use neutral wording and record non-response among selected participants. Increasing a fair sample usually reduces chance variation, but cannot repair exclusion or leading questions. For proportional sampling, allocate places according to each group’s population share, then choose randomly within those groups.
| Year | Students | Sample |
|---|---|---|
| 7 | 200 | 15 |
| 8 | 120 | 9 |
| 9 | 80 | 6 |
See the method in action.
A convenient sample
Students leaving football practice are asked whether the school needs more sports equipment. Can the result represent all students?
Worked solution
- 1
Identify the intended population.
A claim about all students must include students with different activities and interests, including those who do not play football.
- 2
Identify who was actually reached.
Students leaving football practice form a convenience sample that is likely to contain more students interested in sport.
- 3
Explain the likely effect on the result.
This group may place greater value on sports equipment, so its answers cannot reliably represent the whole school.
- 4
Describe a fairer selection method.
Randomly select from the full school roll, possibly within year groups, so non-footballers also have a chance of selection.
Not reliably. The sample is likely to over-represent students interested in sport.
A proportional sample
A school has 200 Year 7, 120 Year 8 and 80 Year 9 students. Allocate a sample of 30.
Worked solution
- 1
Find the population total.
The sample must represent all three year groups.
- 2
Allocate Year 7 places.
Year 7 has half the population, so it receives half the sample places.
- 3
Allocate the other year groups.
Each allocation uses that group’s share of the whole school.
- 4
Check the allocation and select students.
The counts fill the requested sample; random selection within each year group is still needed.
15 Year 7, 9 Year 8 and 6 Year 9 students.
Try it yourself.
Check your understanding
Names are randomly drawn from a list containing only students who own a phone. Is this a fair frame for all students?
Show answer & reasoning
Not reliably.
The frame excludes every student without a phone. Random selection within that incomplete list cannot give those students a chance, so it does not reliably represent all students.
Keep practising
6 worksheet questions · 13 marks
Read the questions online
- A principal surveys 60 of the school's 900 students. Name the population and sample.2 marks
- A gardening-club poll estimates how many town residents grow vegetables. Explain one likely bias.2 marks
- A year group has 180 students in A and 120 in B. Allocate a proportional sample of 50.3 marks
- Explain how to choose a systematic sample of 10 from a list of 100, using a random start.2 marks
- Rewrite neutrally: Do you agree that our excellent new canteen is much better?2 marks
- Forty names are chosen randomly, but only 18 students reply. Why should a report mention this?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A principal surveys 60 of the school's 900 students. Name the population and sample.2 marks
The target is the whole school.
Only 60 students supply responses.
Population: all 900 students. Sample: the 60 surveyed. - A gardening-club poll estimates how many town residents grow vegetables. Explain one likely bias.2 marks
The frame is club users, not all residents.
Interest in gardening is linked to the question.
Gardeners are more likely to see and answer it, so the estimate may be high. - A year group has 180 students in A and 120 in B. Allocate a proportional sample of 50.3 marks
Total is 300.
and .
30 from A; 20 from B. - Explain how to choose a systematic sample of 10 from a list of 100, using a random start.2 marks
The interval is .
The random start avoids always choosing the same initial position.
Randomly select a position from 1 to 10, then take every tenth name. - Rewrite neutrally: Do you agree that our excellent new canteen is much better?2 marks
Remove praise and the suggested answer.
Offer better, about the same, worse and unsure as balanced choices.
How would you rate the new canteen compared with the previous canteen? - Forty names are chosen randomly, but only 18 students reply. Why should a report mention this?2 marks
Only replied.
Random selection does not guarantee representative completed responses.
Non-response may bias the results if respondents differ from non-respondents.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics
Year 9 sampling, comparative distributions, centre/spread/outliers, displays, critique and statistical investigations.
Official curriculum source ↗