Census, sample, experiment or observation

Data can come from everyone (a census), from some (a sample), from an experiment where you change something on purpose, or from watching (an observation). Each has a cost, a time and an accuracy; choose the one that fits the question.

Every five years Australia asks every household the census questions. A TV ratings company measures viewing in only a few thousand homes. Why doesn't it just measure everyone?

The population is everyone (or everything) the question is about. There are four main ways to get data:

Technique	What you do	Example
census	measure every member of the population	the national census of every household
sample	measure some of the population	a poll of 1000 voters
experiment	change something on purpose and measure what happens	half a class revises with music, half without
observation	watch and record without changing anything	counting cars past the school gate

Predict: Read the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.
Try: Try it on the board and compare the result with your prediction.
Investigate: Work out why it happens, one step at a time.
Modify: Change the problem on purpose and see what happens.
Practise: A few on your own, to check you have it.
Make: Make your own problem using what you have learned. Expect a few tries; that is normal.

PredictRead the problem and decide what you think before you try anything. A wrong guess is fine: it shows you what to look for.

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?Exactly the sameNowhere nearClose, but probably not exactly

TryTry it on the board and compare the result with your prediction.

Census and sample

Each dot is a student; the orange rings are the ones measured. The dashed line on the plot is the population's value.

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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.

Use the board. This ticks when you get there.

InvestigateWork out why it happens, one step at a time.

Choosing a technique

Here is the routine for choosing.

Worked exampleBefore each step, say what you think comes next.

$\text{Question: how much do Year 8s spend on lunch?}$ Name the population: Year 8 students.
$\text{Census? } 180 \text{ students: possible, but slow}$ Can you measure everyone? At what cost?
$\text{Sample of } 40 \text{ chosen at random}$ Quicker, cheaper, and close if chosen fairly.
$\text{Not an experiment: nothing is changed}$ Measuring as things are: a survey of a sample.

Read Noah's plan. What does testing a battery do to it?

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?Opinions can't be measuredA sample is more accurate than a censusAsking every person in the city would take too long and cost too muchThe law says so

Noah plans how to collect data. Click the line where his plan goes wrong.

Some students revise with music and some without, chosen at random, then all sit the same test. What technique is this?An observationA censusNot a way to collect dataAn experiment: the researcher changes something on purpose

ModifyChange the problem on purpose and see what happens.

Matching the technique

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Match each situation to the best technique.

Every Australian household fills in a form

A poll of 1000 voters before an election

Plants given different amounts of fertiliser to compare growth

Counting how many birds visit a feeder each hour

Take random samples of 50 students. Are they usually closer to the population than samples of 20?

Use the board. This ticks when you get there.

Why is Australia's census taken only every five years?The population never changesIt costs a great deal and takes months to collect and processFive is a lucky numberA sample would be impossible

A council wants to know how many cars use a road each morning. Which technique fits best?Observation: count the cars as they passExperimentA census of every driver in the stateAsk a sample of drivers to guess

MakeMake your own problem using what you have learned. Expect a few tries; that is normal.

Plan the collection

Choose a question about your school or town, such as "How long do students spend on homework?" or "Does a reminder sign reduce littering?" Write the population, the technique you would use, and one reason it suits the question better than the others.

Need a hint?

Name the population first.

Another hint

Ask: can I measure everyone? Should I change something, or just watch?

I wrote a question, named its population, chose a census, sample, experiment or observation, and explained why it is practical and what it might cost in accuracy.

For teachers

Students compare a census and samples on a simulated school, and choose between census, sample, experiment and observation for real questions (AC9M8ST01, node 1). About 40 minutes.

Open the teacher guide: answers, solutions, slides and a worksheet.

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.

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

Predict: ask what 'close' would mean for a mean of about 9 hours.
Run: ask what the census cost compared with the sample.
Investigate: ask Noah what the factory sells afterwards.
Modify: ask what changed when the sample grew.
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

A student says a sample is always worse. Ask: What would a census of every battery leave? Fix: Samples are chosen for cost, time, or when measuring destroys.
A student calls any survey an experiment. Ask: Did anyone change something on purpose? Fix: Experiment: change one thing and compare. Survey or observation: measure as things are.
A student forgets to name the population. Ask: Who exactly is the question about? Fix: Write the population first: 'all Year 8 students at this school'.

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.

Where it leads

This starts AC9M8ST01.

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

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.

Now you can

Say the difference between a census and a sample.
Tell an experiment from an observation.
Choose a way to collect data and explain why it is practical.

Practise this skillNew questions, new numbers each timeGet 3 right in a row to mark it practised.Next lesson16. Bias in collecting dataBias is anything in the way data is collected that pushes the result one way. It can come from who is asked, how they are asked, or how things are measured, and a bigger sample does not fix it.

Source: content/maths/data/collecting-data/lesson.md