The idea, step by step
The group comes first
A population is the entire group a question concerns. Specify people or objects, place and time: “all Year 8 students enrolled here this term” is clearer than “students”. A census aims to collect data from every unit; a sample uses only a subset. The sampling frame is the list or source used to reach that group.
Coverage matters
A class census may be manageable, while inspecting every factory product may be costly or destructive. A sample must be chosen appropriately. The number invited is not necessarily the number who respond. A large sample of only friends does not automatically represent the whole school.
A common trap
Population always means every person in a country.
Instead: A statistical population is the whole group named by the question, including objects or events.
See the thinking
Worked example 1
A school has 720 students. A lunch survey asks 90 Year 8 students about the whole school. Identify the population and sample.
- The intended population is all 720 students.
- The observed subset is the 90 surveyed Year 8 students.
- Other year levels are missing from the sample.
Worked example 2
A factory inspects 125 of its 2500 bottles made today. What would a census require?
- The population is today’s 2500 bottles.
- 125 is a sample.
- A census would inspect every bottle in that population.
Check your understanding
Every student in a class of 28 answers a question. Census or sample of that class?
Show answer
Census.
All 28 units in the defined population are included.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- A club interviews 40 of its 160 current members. Identify the population and sample.2 marks
- Every one of 36 garden trees is measured. Census or sample of those trees?1 mark
- A survey invites 120 students; 84 reply. What is the response count?2 marks
- A survey uses library visitors to estimate the views of all registered members. Explain a coverage issue.2 marks
- Give one reason a census of a 24-student class is practical.2 marks
- A school samples 20 students from each of six year levels. Find the sample size. Does size alone prove representativeness?3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A club interviews 40 of its 160 current members. Identify the population and sample.2 marks
Distinguish the intended whole group from the observed subset.
Population: all 160 current members; sample: the 40 interviewed. - Every one of 36 garden trees is measured. Census or sample of those trees?1 mark
All 36 trees in the population are measured.
Census. - A survey invites 120 students; 84 reply. What is the response count?2 marks
Invitations and recorded responses are different; 36 did not respond.
84. - A survey uses library visitors to estimate the views of all registered members. Explain a coverage issue.2 marks
The visitor frame differs from all registered members.
Members who rarely visit are not reached by this frame. - Give one reason a census of a 24-student class is practical.2 marks
Including all 24 is manageable and avoids excluding class members.
The small, accessible group can be reached completely. - A school samples 20 students from each of six year levels. Find the sample size. Does size alone prove representativeness?3 marks
20×6=120.
Selection and response still matter.
120; no.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Population, census and sample; observational versus experimental data; random and non-random sampling; primary/secondary data; reviewing numerical displays and summary statistics; comparing samples and sample sizes; bias, variation and uncertainty; planning, conducting and reporting a fair investigation.
Official curriculum source ↗