Bias, variation and uncertainty | Year 8

01 / LEARN

Understand the idea.

Bias has a direction

Bias can systematically favour a result through how data are selected or collected. A gym-only frame can over-represent regular exercisers; leading wording can influence responses. Non-response can also matter when those who reply differ from those who do not.

Ordinary sampling variation is different: fair random samples can disagree without either method favouring a group. An unexpected result is a reason to inspect the method and evidence, not enough by itself to label the study biased or prove a population change.

Do not overstate the evidence

Describe respondents as 'this sample' before generalising. Report the frame, sample size and relevant limitations so readers can judge the reach of a claim. Selective dates, omitted groups or an exaggerated graph scale can make limited evidence look more convincing than it is.

Check unusual observations against the original records. Correct genuine errors, but retain valid unusual values and explain their effect on summaries. Deleting inconvenient values merely to make a result look sensible introduces a new problem instead of resolving uncertainty.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

A gym survey finds 90% exercise daily. Can it be confidently generalised to all students?

Worked solution

1
Compare the survey frame with the target group.
The claim concerns all students, but a gym survey reaches gym visitors.
2
Explain why the omitted students matter.
Gym visitors are plausibly more likely to exercise daily than students who do not visit, so the frame may overstate the proportion.
3
Limit the 90% claim.
$90 % describes the surveyed group$
It cannot confidently describe all students without broader sampling; increasing a gym-only sample would retain the selection problem.

Answer

No; selection bias is likely.

EXAMPLE 02

Worked example 2

Two fair samples of 50 find 27 and 31 supporters. Compare their percentages.

Worked solution

1
Calculate the first percentage.
$\frac{27}{50} \times 100 % = 54 %$
Twenty-seven supporters are out of the first fifty respondents.
2
Calculate the second percentage.
$\frac{31}{50} \times 100 % = 62 %$
Thirty-one supporters are out of a different sample of fifty.
3
Measure the percentage-point gap.
$62 - 54 = 8 percentage points$
Subtracting percentages gives a percentage-point difference, not an 8% relative increase.
4
State what the comparison establishes.
The observed samples differ, but ordinary sampling variation could explain that gap; a population change has not been proved.

Answer

54% and 62%; a population change is not proved.

03 / YOUR TURN

Try it yourself.

Check your understanding

What is wrong with “Don’t you agree our excellent canteen deserves more funding?”

Show answer & reasoning

Leading wording.

The phrases 'Don't you agree' and 'excellent canteen' suggest approval before the person answers. This leading wording may influence responses rather than neutrally measure views.

Keep practising

6 worksheet questions · 15 marks

Open worksheet Worked solutions

Read the questions online

Rewrite “Don’t you agree homework is a waste of time?” neutrally.
2 marks
Of 100 invitees, 40 reply and 24 say yes. Find the yes percentage among respondents and state a limitation.
3 marks
A fair sample of 40 includes 12 walkers. Estimate the number among 800 students and state a limitation.
3 marks
Must one calculation be wrong if two random samples have different means?
2 marks
A report calls the single week with the longest queue typical. Explain the concern.
2 marks
Give a transparent way to discuss a valid outlier.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Rewrite “Don’t you agree homework is a waste of time?” neutrally.
2 marks
Remove the suggested judgement.
For example: “How useful do you find homework?” with balanced response options.
Of 100 invitees, 40 reply and 24 say yes. Find the yes percentage among respondents and state a limitation.
3 marks
$\frac{24}{40} \times 100 = 60 %$ .
The remaining 60 invitees have not supplied answers.
60%; non-respondents’ views are unknown.
A fair sample of 40 includes 12 walkers. Estimate the number among 800 students and state a limitation.
3 marks
$\frac{12}{40} = 0.3$ .
$0.3 \times 800 = 240$ .
About 240; another fair sample may differ.
Must one calculation be wrong if two random samples have different means?
2 marks
Ordinary sampling variation is possible.
No. Different sampled values can correctly produce different means.
A report calls the single week with the longest queue typical. Explain the concern.
2 marks
Selective timing can promote a misleading conclusion.
An exceptional selected period may not represent ordinary conditions.
Give a transparent way to discuss a valid outlier.
3 marks
Do not silently remove inconvenient valid data.
Report it, examine its effect, and explain any comparison with and without it.

Checking saved progress…

Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum

Population, census and sample; observational versus experimental data; random and non-random sampling; primary/secondary data; reviewing numerical displays and summary statistics; comparing samples and sample sizes; bias, variation and uncertainty; planning, conducting and reporting a fair investigation.

Official curriculum source ↗

In this lesson

Understand the idea.

Bias has a direction

Do not overstate the evidence

See the method in action.

Worked example 1

Compare the survey frame with the target group.

Explain why the omitted students matter.

Limit the 90% claim.

Worked example 2

Calculate the first percentage.

Calculate the second percentage.

Measure the percentage-point gap.

State what the comparison establishes.

Try it yourself.

Check your understanding

Keep practising