The idea, step by step
Bias can enter before a graph exists
A convenience sample may exclude important groups. A voluntary survey can attract people with strong views. A leading question can push people toward an answer. These issues affect how well the resulting data represent the intended population.
Increasing the sample size does not automatically remove selection bias. A large survey taken from the wrong group may be less useful than a smaller well-designed sample.
Presentation and wording matter
Check axes, units, baselines and intervals. A truncated vertical axis may exaggerate a difference in a bar chart; an unequal interval scale may distort a trend. Averages can hide variability, and a percentage change can sound dramatic when based on very small counts.
Critique precisely rather than dismissing every unusual graph. A limited axis can be appropriate for a time-series detail when clearly shown. Ask what the display claims and what the supplied data actually justify.
A common trap
A survey with thousands of responses cannot be biased.
Instead: Large size reduces some random variation, but does not repair systematically excluded groups or leading questions.
See the thinking
A restricted survey
A school asks only students at basketball training whether the school should buy more basketball equipment. What is the issue?
- The target may be all students, but only basketball participants were sampled.
- This group may be more favourable to the purchase.
- A sample across the school would better address school-wide preference.
A dramatic percentage
Complaints rose from 2 to 4. A headline says complaints 'soared by 100%'. Is the arithmetic correct, and what context is missing?
- The increase is 2 and the original count is 2.
- 2/2×100=100%, so the percentage is correct.
- The small absolute counts and time/population context matter.
Check your understanding
A bar chart compares 100 and 102 but starts its vertical axis at 99. What may happen visually?
Show answer
The small difference can appear much larger.
The displayed bar heights exaggerate the difference relative to the full values.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- A website polls only its subscribers about national voting intentions. Name a risk.2 marks
- Rewrite this leading question neutrally:'Do you agree our excellent new timetable should stay?'2 marks
- Sales rose from 20 to 25. Find the absolute and percentage increase.3 marks
- A report gives a mean income but no sample size, spread or sampling method. Name two useful additions.2 marks
- A graph uses month 1, month 2, month 10 at equal horizontal spacing. Explain the distortion.2 marks
- Why should you not delete an extreme value just to make a claim look stronger?3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A website polls only its subscribers about national voting intentions. Name a risk.2 marks
The sampling frame is restricted.
Many voters have no opportunity to participate.
Selection bias: subscribers may not represent all voters. - Rewrite this leading question neutrally:'Do you agree our excellent new timetable should stay?'2 marks
Remove the approving adjective'excellent'.
Offer balanced response options.
For example:'Should the new timetable stay or change?' - Sales rose from 20 to 25. Find the absolute and percentage increase.3 marks
25−20=5.
5/20×100=25%.
Increase 5; 25%. - A report gives a mean income but no sample size, spread or sampling method. Name two useful additions.2 marks
A mean alone does not establish representativeness.
Additional context supports interpretation.
For example, sample size and a spread measure/sampling method. - A graph uses month 1, month 2, month 10 at equal horizontal spacing. Explain the distortion.2 marks
The gaps are 1 month and 8 months.
The apparent rate of change is distorted.
Unequal time intervals are displayed as equal distances. - Why should you not delete an extreme value just to make a claim look stronger?3 marks
Check errors and context.
Report the rule and its effect on the conclusion.
It may be genuine evidence; exclusion needs a stated, defensible reason.
Curriculum reference & lesson scope
Australian Curriculum v 9 and SA Curriculum Mathematics
Year 10 continuous distributions, bivariate data, two-way categorical tables, bias and investigations, with the approved percentile and standard-deviation content included in the normal chapter.
Official curriculum source ↗