The idea, step by step
Define the whole group
The population is the entire group the question concerns. A sample is the part measured. A census attempts to collect data from every member of a defined population. Name the group and the relevant date or period; “all people” is usually too vague.
A census avoids selecting only part of the group, but can still suffer non-response or inaccurate measurement. It is not automatically free of error.
Keep statistics and parameters distinct
A parameter describes a population, such as mean travel time of all 420 cohort members. A statistic is calculated from a sample, such as the mean of 60 selected students. A well-designed statistic can estimate the unknown parameter.
The sampling frame is the list used for selection. A school email list may omit recent enrolments or people without working access. A mismatch between frame and target population can limit conclusions.
A common trap
A sample of 100 represents every population equally well.
Instead: Selection method and coverage matter as well as size.
See the thinking
Identify four quantities
A club has 240 members. Forty randomly selected members average 5.2 training hours weekly.
- Population is all 240 members.
- Sample is the 40 measured members.
- 5.2 describes the sample; the mean of all 240 is the unknown parameter.
Choose a practical design
A factory must open and destroy a container to test its contents. Why sample 500 containers rather than test all?
- A census would destroy the entire batch.
- A well-selected sample reduces the destruction, with uncertainty about untested items.
Check your understanding
All 86 staff are asked about parking, but 70 respond. Is this a completed census?
Show answer
No.
It is an attempted census with 16 missing responses.
Your turn
6 questions · 12 marks · Work at your own pace.
Read the questions online
- Seventy-five of 3,200 registered library users are surveyed. Identify population and sample.2 marks
- Those 75 users have median 3 visits monthly. Is 3 a parameter?2 marks
- A teacher asks all 28 class members for shoe size; 23 respond. Is this complete?2 marks
- Give a reason to census a 12-person team for equipment sizes.2 marks
- Online ticket buyers are surveyed to describe all concert attendees. Identify a frame concern.2 marks
- Why can a census of self-reported income still mislead?2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Seventy-five of 3,200 registered library users are surveyed. Identify population and sample.2 marks
Use the intended group and observed subset.
Population: 3,200 users; sample: 75 surveyed users. - Those 75 users have median 3 visits monthly. Is 3 a parameter?2 marks
It describes only the measured sample.
No, it is a sample statistic. - A teacher asks all 28 class members for shoe size; 23 respond. Is this complete?2 marks
Attempting a census does not remove non-response.
No; five responses are missing. - Give a reason to census a 12-person team for equipment sizes.2 marks
A small accessible group can make a census practical.
All are easily contacted and each response affects ordering. - Online ticket buyers are surveyed to describe all concert attendees. Identify a frame concern.2 marks
The frame may not cover the target population.
Venue and other-seller buyers may be excluded. - Why can a census of self-reported income still mislead?2 marks
Complete coverage does not ensure accurate measurement.
Responses may be inaccurate or inconsistently defined.
Curriculum reference & lesson scope
SACE Board of South Australia
Stage 1 General Mathematics: statistical investigation, univariate data, sampling, displays, summaries and interpretation.
Official curriculum source ↗