Understand the idea.
Find the evidence behind the headline
Separate a headline's claim from its evidence. Identify who was asked, how many people answered, when the data was collected and the exact question. Then ask whether the claim is about those people or about a much wider group.
If eighteen of twenty club members like chess, that is of those surveyed members. It does not establish the preference of the whole school: members of one club may have different interests from students outside it.
Check scales and comparisons
Read the actual scale before judging a graph. On an axis beginning at , counts of and rise only and above the baseline. The visible bars can suggest a doubling even though the counts have not doubled.
Compare like quantities and identify each percentage's whole group. Twenty absent students can be a different proportion in two schools of different sizes. Describe the evidence carefully; observing two things together does not by itself explain what caused either one.
See the method in action.
A claim that goes too far
A headline says Everyone wants a longer lunch. Its evidence is 12 of 15 students from one sports team. Is the headline supported?
Worked solution
- 1
Identify what everyone would require.
The headline claims that every person in its audience wants a longer lunch.
- 2
Check the surveyed team's answers.
Three surveyed team members did not support the claim, so even this team was not unanimous.
- 3
Check who was left out.
The survey includes only one sports team, so it cannot establish the wishes of students outside that team.
- 4
State the supported conclusion.
The evidence supports twelve of fifteen surveyed team members wanting a longer lunch; it does not support everyone.
No. The data supports 12 of 15 surveyed team members, not everyone.
Equal counts, different proportions
School A has 20 absent students out of 100. School B has 20 absent students out of 200. Are the absence proportions equal?
Worked solution
- 1
Find School A's absent proportion.
The whole group for School A is one hundred students.
- 2
Find School B's absent proportion.
The same absent count is shared across a group twice as large.
- 3
Compare the percentages.
The proportions are unequal: School A has one fifth absent, while School B has one tenth absent.
No. A has 20% absent and B has 10%.
Try it yourself.
Check your understanding
A survey asks five friends about a new playground. Can it prove every child likes the playground?
Show answer & reasoning
No.
A survey of five friends records only those friends' views. Even agreement among all five cannot establish the opinion of every child, because children outside that group were not asked.
Keep practising
6 worksheet questions · 11 marks
Read the questions online
- A report says all 30 students chose apples, but its table records 24 apples and 6 pears. Is the report correct?1 mark
- A shop says 9 of 10 surveyed customers liked a product. What important group should the claim name?2 marks
- A chart begins its vertical axis at 90 and shows values 96 and 100. What is the actual difference?2 marks
- Compare 6 of 10 students with 6 of 20 students as percentages.2 marks
- A table shows more ice creams sold on hotter days. Does this alone prove buying ice cream makes the weather hotter?2 marks
- A class asked only students arriving by bicycle whether the school needs more bicycle racks. Suggest one way to improve the evidence.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A report says all 30 students chose apples, but its table records 24 apples and 6 pears. Is the report correct?1 mark
The six pear choices contradict the word all.
No. Twenty-four chose apples, not all 30. - A shop says 9 of 10 surveyed customers liked a product. What important group should the claim name?2 marks
The claim should not be extended to every person or every customer without evidence.
The surveyed customers. - A chart begins its vertical axis at 90 and shows values 96 and 100. What is the actual difference?2 marks
Subtract the values: .
Read the scale instead of judging the visible bar lengths.
4. - Compare 6 of 10 students with 6 of 20 students as percentages.2 marks
.
.
and . - A table shows more ice creams sold on hotter days. Does this alone prove buying ice cream makes the weather hotter?2 marks
The table shows the quantities vary together.
It does not show that ice-cream purchases cause hotter weather.
No. - A class asked only students arriving by bicycle whether the school needs more bicycle racks. Suggest one way to improve the evidence.2 marks
The original group is likely to have particular views about bicycle racks.
A broader group makes the limitations clearer. Other reasonable improvements are acceptable.
Ask a wider set of students, including people who arrive by other methods.
Curriculum reference & lesson scope
Australian Curriculum v9.0; SA Mathematics Curriculum 2026
Variable types; comparative displays; mode/range/shape; media claims; investigations.
Official curriculum source ↗