The idea, step by step
Find the evidence behind the headline
A claim may be true for the people measured but too broad for everyone else. Ask who supplied the data, how many observations there were, when they were collected and whether the question was fair.
If 18 of 20 club members like chess, that supports a claim about those members. It does not establish that 90% of every student in the school likes chess. We have not asked the other students.
Check scales and comparisons
A graph with a vertical axis beginning at 40 can make counts 45 and 50 look very different. Read the axis values, not just the apparent heights. A broken or shortened scale needs to be made clear.
Percentages also need a reference group. A rise from 10 to 20 is ten more and twice the original amount; a rise from 100 to 110 is also ten more but a much smaller relative change. Look for what is being compared and avoid claiming a cause from a simple pattern.
A common trap
A large-looking difference between bars must be a large difference in the data.
Instead: Read the scale and actual values; bar appearance can exaggerate a small change.
See the thinking
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?
- Twelve of fifteen is a majority of that team.
- It is not every team member, and students outside the team were not asked.
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?
- School A: .
- School B: .
- The same absent count represents different parts of the two schools.
Check your understanding
A survey asks five friends about a new playground. Can it prove every child likes the playground?
Show answer
No.
Only five friends were asked; their answers cannot establish what every child thinks.
Your turn
6 questions · 11 marks · Work at your own pace.
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
.
.
60% and 30%. - 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 ↗