Understand the idea.
The group comes first
Start with the question's population: the complete group the conclusion is meant to describe. Include the place and period, such as all Year 8 students enrolled at this school this term. A population can contain objects or events as well as people.
A census aims to obtain information from every member of that defined group. A sample contains only some members. The sampling frame is the list or source used to reach them; check whether it actually covers the intended population.
Coverage matters
Choose between a census and sample by considering time, cost and what measurement involves. Counting a small class may be practical; testing every product may be expensive or destroy the products. Sampling can help, but its selection method still matters.
Distinguish people selected, people invited and people who actually respond. Missing year levels or non-responders can limit the conclusion. Surveying many friends does not correct the exclusion of students outside that friendship group.
See the method in action.
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.
Worked solution
- 1
Identify whose lunches the conclusion concerns.
The question is about the whole school, so all 720 students form the population.
- 2
Identify the observed subset.
Only the 90 surveyed Year 8 students supply responses; they form the sample.
- 3
Check whether the frame covers the population.
Other year levels have been excluded, so these 90 responses may not represent all 720 students.
Population 720; sample 90; coverage is limited.
Worked example 2
A factory inspects 125 of its 2500 bottles made today. What would a census require?
Worked solution
- 1
Define the population by production day.
The study concerns the 2500 bottles made today, not every bottle the factory has ever made.
- 2
Classify the current inspection.
Inspecting only 125 bottles uses a subset, so it is a sample.
- 3
State what complete coverage requires.
A census must inspect every bottle in today's population.
All 2500 bottles.
Try it yourself.
Check your understanding
Every student in a class of 28 answers a question. Census or sample of that class?
Show answer & reasoning
Census.
The population is the class of 28, and every one of those 28 students answers. Complete coverage of this defined group makes it a census.
Keep practising
6 worksheet questions · 12 marks
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
.
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 ↗