Students see a convenience sample miss the population on a simulated school, then name and fix sampling, response and measurement bias in real plans (AC9M8ST01, node 2).
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Students will be able to
I can spot bias in the way data is collected.
I can say which way a bias pushes the result.
I can change a plan to make it fairer.
Timing
Predict and Run 8 min · Investigate 12 min · Modify 10 min · Practise and Make 10 min
Before class
Do the Run board yourself first. Students need census and sample (last lesson).
The one idea: bias comes from who is asked (sampling), how they are asked (response) or how it is measured (measurement), and it pushes the result one way. The common mistake is thinking a big sample cancels bias (the radio phone-in).
The board's convenience sample is the students nearest the door: the Year 7 rows. Year 7s play more sport and sleep more, so the result is pushed up.
Wider: the 1936 Literary Digest poll (over 2 million replies, wrong winner) is the classic large biased sample.
Running the lesson
Predict: ask who is in the library at lunch.
Run: ask which year groups the convenience sample holds.
Investigate: ask who chooses to phone a radio station.
Modify: ask whether growing the sample changed who is in it.
Make: ask for one fix for each bias.
The hard part (on purpose)
Saying which way the bias pushes. Ask: compared with everyone, would this group answer higher or lower?
When students get stuck
What you will see
A question to ask
The fix
A student says the sample is fine because it is big.
Who is in it? Would more of the same people change that?
Size reduces chance error, not bias.
A student can name bias but not its direction.
Would this group answer higher or lower than everyone?
Say the direction: 'too high because...'.
A student calls any small sample biased.
Was anyone more likely to be chosen than others?
Small random samples vary, but they aren't biased; biased means pushed one way.
Answers to the checks
the library survey: Students in the library at lunch are asked: 'Does the school need a bigger library?' How will the result compare with what the whole school thinks? Too many yes answers, most likely. Students who choose the library at lunch are more likely to want a bigger one.
who you ask: Take a convenience sample (the 20 nearest the door) and look where it lands. Then take a simple random sample of 20. Which is closer to the whole school? Was your prediction's reasoning the same?
The convenience sample is all Year 7, who play more sport: its proportion is too high. A random sample gives every student the same chance.
Kinds of bias: Which kind of bias is each? Surveying football fans about the town's favourite sport → Who is asked (sampling bias); Asking 'Don't you agree litter is a disgrace?' → How they are asked (response bias); Weighing parcels on scales that read 200 g too heavy → How it is measured (measurement bias); Asking students in front of their teacher how much homework they really do → How they are asked (response bias); Only people who chose to reply to an online poll (they selected themselves) → Who is asked (sampling bias) Sampling bias: the sample isn't like the population. Response bias: the question or setting pushes answers. Measurement bias: the tool or method is off.
Find the mistake: A radio station runs a poll. Click the line where the reasoning goes wrong. line 3 Line 3: the callers chose themselves, and people who want a change are more likely to call. 1200 biased answers are still biased: a bigger sample doesn't fix bias.
A fairer library survey: How could the library survey be made less biased? Ask students chosen at random from the whole school roll Random choice from the whole population gives every student the same chance of being asked.
Bigger convenience sample: Make the convenience sample 80 or bigger. Is it still too high?
Even 80 students from the front rows are mostly Years 7 and 8, who play more sport. More of a biased sample stays biased.
Leading question: A survey asks: 'Would you support a new skate park, which would keep teenagers busy and off the streets?' What is the problem? It is a leading question: it gives reasons to say yes A fair question doesn't argue for one answer: 'Would you support a new skate park?'
Faulty tape: A class measures their heights with a tape whose first 2 cm has been cut off, so it reads 2 cm too much. What happens to the mean height? Every height is 2 cm too high: measurement bias A faulty tool shifts every value the same way, so the mean is wrong by the same amount.
Honest answers: Which reduces response bias in a survey about cheating on tests? Answers are anonymous People answer more honestly when no one can tell which answer is theirs.
Screen time: To find how much screen time teenagers have, a researcher surveys students at a gaming expo. The result is likely to be: Too high People at a gaming expo probably have more screen time than teenagers in general: sampling bias.
Online poll: An online poll gets 50 000 votes. Why might it still be biased? Voters choose themselves, so people who care a lot are overrepresented Self-selected samples are biased however big they are.
A fair sample: Which is a fair sample of 30 from a school's 600 students? 30 students picked by a random number generator from the roll Random choice from the whole roll gives every student the same chance.
Review: technique: Review: scientists give half the tomato plants a new plant food and compare their growth. What technique is this? Experiment Changing something on purpose and comparing is an experiment.
Solutions
One possible solution for each task. Other correct programs are fine.
does a bigger sample help? › Bigger convenience sample
Open task: any program that does what the step asks.
does a bigger sample help? › Leading question
Open task: any program that does what the step asks.
does a bigger sample help? › Faulty tape
Open task: any program that does what the step asks.
does a bigger sample help? › Honest answers
Open task: any program that does what the step asks.
Stretch and support
Stretch: Research the 1936 Literary Digest poll. How could 2.4 million replies get the winner wrong?
Support: A card with the three kinds of bias and a question to ask for each: who? how asked? how measured?
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 "Bias in collecting data".
The idea: Bias in data collection: I can Students recognise and explain sources of bias in data collection and describe how bias affects conclusions.
What understanding looks like:
- Identifies a source of bias in a data collection scenario.
- Explains the likely direction and effect of the bias.
- Suggests a concrete method to reduce the identified bias.
Mistakes students often make here:
- A student says the sample is fine because it is big.
- A student can name bias but not its direction.
- A student calls any small sample biased.
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.
- If I seem to be missing the idea that comes before this one (Census vs sampling and collection technique selection), check it quickly, then come back.
- 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 "Bias in collecting data".
Exit ticket
A gym surveys its members on how often people exercise. Name the bias and which way it pushes the result.
Sampling bias: gym members exercise more than most people, so the result is too high.
What each step is for
the library survey: Committing to how a library survey answers 'do we need a bigger library?' shows whether they see who was asked.
who you ask: A convenience sample from one corner of the school gives a result pushed one way; a random sample does not.
kinds of bias: Bias comes from who is asked, how they are asked, or how things are measured; a big biased sample is still biased (the radio poll).
does a bigger sample help?: Growing a convenience sample doesn't remove its bias, while leading questions and faulty tools bias any sample.
spotting bias: Naming the source and direction of bias in new plans, mixed; thinking a big sample cancels bias is the planted slip; techniques are the review.
fix a biased survey: Rewriting a biased plan to remove each kind of bias shows they can design fairly.
Where it leads
This completes AC9M8ST01.
Where it leads: sampling methods (next), and investigations with samples.