Understand the idea.
Define the whole group
The population is the whole group the question concerns; the sample is the subset measured. Name the group and time boundary before counting it. A census seeks a response from every population member.
An attempted census is incomplete when some members do not respond. Even a completed census can contain inaccurate measurements or misunderstood questions, so complete coverage and accurate data are separate requirements.
Keep statistics and parameters distinct
A statistic describes a sample; a parameter describes the population. A sample mean estimates a population mean, but the two need not be equal. The statistic is known from the records; the parameter may remain unknown.
The sampling frame is the list from which people are selected. If it omits recent enrolments, those students cannot be selected. Check the frame against the intended population before treating the sample as representative.
See the method in action.
Identify four quantities
A club has 240 members. Forty randomly selected members average 5.2 training hours weekly.
Worked solution
- 1
Identify the population and sample.
All club members form the population; only the forty selected members were measured.
- 2
Classify the observed average.
This mean uses the sample, so it is a statistic.
- 3
Name the corresponding parameter.
The population mean concerns everyone in the club and is not supplied by the sample result.
Population 240; sample 40; statistic 5.2 hours; parameter the population mean.
Choose a practical design
A factory must open and destroy a container to test its contents. Why sample 500 containers rather than test all?
Worked solution
- 1
Consider what a census would require.
Testing every container would destroy every container in the batch.
- 2
Explain the advantage of the sample.
Testing a selected subset leaves the other containers available while providing evidence about the batch.
- 3
State what remains uncertain.
Untested containers were not individually checked, so the sample cannot prove that every one is safe.
Destructive testing favours sampling; it cannot prove every untested item is safe.
Try it yourself.
Check your understanding
All 86 staff are asked about parking, but 70 respond. Is this a completed census?
Show answer & reasoning
No.
No. Asking everyone is an attempted census, but responses are missing. The completed data cover only the seventy respondents.
Keep practising
6 worksheet questions · 12 marks
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 ↗