Understand the idea.
Bias can enter before a graph exists
Selection bias occurs when the way people enter a sample systematically favours some groups or opinions. Convenience samples can omit relevant people; voluntary surveys can attract strong views. A leading question can also influence the responses obtained.
First identify the population the claim concerns, then ask who actually had a chance to respond. Increasing a biased sample may reduce random fluctuation around an unrepresentative result; it does not repair the systematic exclusion.
Presentation and wording matter
Inspect how the evidence is presented: units, equal scale intervals, axis baselines and the groups or periods compared. Bar lengths measured from a truncated baseline can make small differences look dramatic. Clearly labelled restricted axes may serve other display purposes, so critique the particular claim.
Check both relative and absolute change. A large percentage rise can come from tiny starting counts. Ask for the counts, time period and relevant population size before interpreting its practical significance; correct arithmetic alone cannot supply missing context.
See the method in action.
A restricted survey
A school asks only students at basketball training whether the school should buy more basketball equipment. What is the issue?
Worked solution
- 1
Identify the population implied by the decision.
A school-wide equipment decision may concern the preferences of all students.
- 2
Compare that population with the sample.
Only basketball trainees were asked; other students had no representation in the sample.
- 3
Explain the likely limitation and improvement.
Trainees may favour basketball spending more than others. Sampling across the school would better support a whole-school claim.
Selection bias limits a whole-school conclusion.
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?
Worked solution
- 1
Find the absolute increase.
Absolute change states how many additional complaints occurred.
- 2
Calculate change relative to the original count.
Percentage increase uses the starting count as its denominator, so the headline's arithmetic is correct.
- 3
Identify the missing context.
The increase is only two complaints. Comparable time periods and population sizes are needed to judge how meaningful that change is.
Correct percentage, but the increase was only 2 complaints and needs context.
Try it yourself.
Check your understanding
A bar chart compares 100 and 102 but starts its vertical axis at 99. What may happen visually?
Show answer & reasoning
The small difference can appear much larger.
Above a baseline of , the displayed heights are and . That makes a small difference in full values look much larger through bar length.
Keep practising
6 worksheet questions · 14 marks
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
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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 ↗