Census, sample, experiment or observation

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

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Students will be able to

• I can say the difference between a census and a sample.
• I can tell an experiment from an observation.
• I can choose a way to collect data and explain why it is practical.

Timing

Predict and Run 8 min · Investigate 10 min · Modify 12 min · Practise and Make 10 min

Before class

Do the Run board yourself first. Students need statistical questions and investigations from Year 7.

The one idea: a census is exact but often slow, costly or impossible; a sample estimates; an experiment changes something on purpose; an observation watches. The common mistake is thinking a census is always best (Noah's battery test destroys what it measures).

The board is a made-up school of 200 students (the same every time): sleep falls and sport drops with year level, which matters in the next lessons on bias and sampling methods.

Wider: the ABS census and the monthly Labour Force Survey (a sample of about 50 000 people) as a real pair.

Running the lesson

1. Predict: ask what 'close' would mean for a mean of about 9 hours.
2. Run: ask what the census cost compared with the sample.
3. Investigate: ask Noah what the factory sells afterwards.
4. Modify: ask what changed when the sample grew.
5. Make: ask what you would give up by not measuring everyone.

The hard part (on purpose)

Weighing cost against accuracy. Ask: what would it take to measure everyone, and is it worth it?

When students get stuck

Answers to the checks

1. a sample of 20: A school has 200 students. You ask 20 of them, chosen at random, how long they sleep. Will their mean equal the mean of all 200?
   Close, but probably not exactly. A random sample gives an estimate; a census gives the exact value, at much more cost.
2. census and sample: First, if you like, take a census (press Census, then Take a census). Then press Simple random and take a sample of 20. How close is it to the population's mean (the dashed line)? Compare with your prediction.
   
   The census gives the population's mean exactly. A random sample of 20 is usually within a few tenths of an hour.
3. Why a sample: A newspaper wants to know what people in its city think of a new bridge. Why does it survey a sample of 800, not everyone?
   Asking every person in the city would take too long and cost too much
   When measuring everyone costs too much or takes too long, a fair sample is the sensible choice.
4. Find the mistake: Noah plans how to collect data. Click the line where his plan goes wrong.
   line 2
   Line 2: testing every battery until it is flat leaves the factory nothing to sell. Test a sample instead.
5. Experiment: Some students revise with music and some without, chosen at random, then all sit the same test. What technique is this?
   An experiment: the researcher changes something on purpose
   The music is the thing changed on purpose; the scores show its effect.
6. Match the technique: Match each situation to the best technique.
   Every Australian household fills in a form → B. census; A poll of 1000 voters before an election → C. sample; Plants given different amounts of fertiliser to compare growth → A. experiment; Counting how many birds visit a feeder each hour → D. observation
   Census: everyone. Sample: some. Experiment: change something. Observation: watch without changing.
7. Bigger samples: Take random samples of 50 students. Are they usually closer to the population than samples of 20?
   
   Bigger samples usually land closer to the population's value, at more cost.
8. The census: Why is Australia's census taken only every five years?
   It costs a great deal and takes months to collect and process
   A census of millions of homes is expensive and slow. Smaller samples (such as the monthly Labour Force Survey) fill the gaps.
9. Counting cars: A council wants to know how many cars use a road each morning. Which technique fits best?
   Observation: count the cars as they pass
   Watching and counting, without changing anything, is an observation.
10. Small class: A teacher wants the mean height of her class of 25. What is most sensible?
    A census: measuring 25 students is quick
    When the population is small and measuring is easy, a census gives the exact answer.
11. Toothpaste: A company wants to know if a new toothpaste reduces cavities. What technique fits?
    An experiment: some use the new toothpaste, some the old, chosen at random
    To see the effect of a change, compare groups given different treatments.
12. Testing every bottle: A juice factory checks the sugar in its bottles. A manager says: 'Test every bottle, so we know for sure.' What is wrong with that plan?
    Testing opens the bottle, so there would be nothing left to sell
    When measuring destroys the item, a sample is the only sensible choice.
13. Review: complement: Review: a spinner has equal parts red, blue, green and yellow. What is P(not red)?
    3/4
    1 − 1/4 = 3/4.

Solutions

One possible solution for each task. Other correct programs are fine.

matching the technique › Match the technique

Open task: any program that does what the step asks.

matching the technique › Bigger samples

Open task: any program that does what the step asks.

matching the technique › The census

Open task: any program that does what the step asks.

matching the technique › Counting cars

Open task: any program that does what the step asks.

Stretch and support

Stretch: Find out how the ABS chooses the homes in the Labour Force Survey, and why it doesn't ask the same homes forever.

Support: The four techniques on a card, each with a picture example.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 8 student in Australia. Help me understand ONE idea only, from the lesson "Census, sample, experiment or observation".

The idea: Census vs sampling and collection technique selection: I can Students distinguish census from sampling and identify when each is appropriate; describe the main data collection techniques.

What understanding looks like:
- Correctly distinguishes census from sampling.
- Identifies an appropriate collection technique for a given context and justifies the choice.
- Explains at least one practical limitation of sampling.

Mistakes students often make here:
- A student says a sample is always worse.
- A student calls any survey an experiment.
- A student forgets to name the population.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Census, sample, experiment or observation".

Exit ticket

A cereal company wants to check the weight of its boxes. Census or sample? Why?

A sample: weighing every box costs time; checking a random sample of boxes each hour is enough to spot problems.

What each step is for

• a sample of 20: Committing to how a sample's mean compares with the population's shows whether they expect samples to be exact.
• census and sample: Taking a census and then a sample on the same school shows a census is exact and a sample is quicker but close.
• choosing a technique: A census isn't possible or sensible when measuring destroys, costs or takes too long (Noah); an experiment changes something, an observation doesn't.
• matching the technique: Matching situations to techniques, then seeing that a bigger sample gets closer, shows cost against accuracy.
• techniques: Choosing and justifying techniques in new contexts, mixed; a census that destroys what it measures is the planted slip; probability is the review.
• plan the collection: Choosing a technique for their own question and saying why shows they can weigh practicality and accuracy.

Where it leads

This starts AC9M8ST01.

Where it leads: bias in data collection (next), sampling methods, and investigations with samples.