Graphs, data and probability
Misleading graphs: check the scale and the claim
Spot truncated axes, unfair comparisons and unsupported conclusions. Practise checking graph claims with six questions and fully explained answers.
Grades 6–7 practice · 6 questions · Free to print · Answers included
Make sense of the method
A graph can use correct numbers and still create a misleading impression. Check the baseline, intervals, sample and exact words of the claim.
A non-zero axis may help examine small differences, but bar lengths then do not show the ratios of the full values. The axis must be clear.
- Read the actual numbers and units before judging bar lengths.
- Check whether the scale starts at zero and uses equal intervals.
- For a claim about ‘twice as much’, divide full values rather than visible heights above a shortened baseline.
- Check who was measured, how they were selected and whether comparison groups have the same size.
A worked example
A chart shows 18 visits on Saturday and 24 on Sunday, but its axis begins at 12. Someone says Sunday had twice as many visits because its bar looks twice as tall. Check the claim.
- Above the baseline, the visible heights represent 18 − 12 = 6 and 24 − 12 = 12.
- The full counts are 18 and 24, so the correct ratio is 24/18 = 4/3.
- A zero-baseline bar chart would show the full counts proportionally.
False: Sunday had 4/3 as many visits, not twice as many.
Try the worksheet
Start with the first two questions, then build toward the final challenge. Show your method with calculations, drawings or a short explanation. These are practice questions with published answers, not a full-topic readiness check.
Build the foundation
1.Where does this vertical axis begin, and how many centimetres does one labelled interval represent?
Show your work on paper.Build the foundation
2.Find the actual difference between the two recorded heights. Show your calculation.
Show your work on paper.Strengthen your method
3.A caption says ‘Tray B is two and a half times as tall as Tray A.’ Explain how the cropped bars create this impression, then find the actual height ratio.
Show your work on paper.Strengthen your method
4.Redraw the seedlings graph with a zero baseline and a uniform scale reaching at least 48 cm. Keep both values and units. Give one accurate comparison as a replacement caption.
Show your work on paper.Apply and explain
5.Invented survey table: Club A has 12 supporters among 20 members; Club B has 18 supporters among 40 members. A graph of supporter counts claims support is more widespread in Club B. Compare both counts and percentages. Is that conclusion justified?
Show your work on paper.Apply and explain
6.A school has 300 students. At a lunchtime chess club, 24 of 30 students surveyed prefer chess to running. A poster says ‘80% of the school prefers chess.’ Check the percentage and explain the sampling problem. Suggest a better way to investigate the school-wide question.
Show your work on paper.
Worked answers
Try the questions first. Then compare the reasoning, not just the final result.
Show all six worked solutions
1. It begins at 38 cm; each interval is 2 cm.
- Read the bottom label, 38, rather than assuming zero.
- Adjacent labels increase by 2, for example 38 to 40.
2. 6 cm.
- Tray A is 42 cm and Tray B is 48 cm.
- 48 − 42 = 6 cm.
3. The visible-height ratio is 10/4 = 2.5; the actual ratio is 48/42 = 8/7, about 1.14.
- Above 38 cm, the bars represent 42 − 38 = 4 and 48 − 38 = 10.
- 10 ÷ 4 = 2.5 describes these cropped lengths, not the seedlings.
- Using full heights gives 48/42 = 8/7 ≈ 1.14. The caption is false.
4. Use bars at 42 cm and 48 cm from zero. One accurate caption is ‘Tray B is 6 cm taller than Tray A.’
- Choose a uniform scale such as 0, 10, 20, 30, 40, 50 cm.
- Draw equal-width bars ending at 42 and 48, with labelled categories and units.
- 48 − 42 = 6 cm. Other accurate comparisons and uniform scales are valid.
5. Club B has more supporters, but Club A has the larger percentage: 60% versus 45%.
- Counts: 18 is greater than 12.
- Club A: 12/20 × 100 = 60%. Club B: 18/40 × 100 = 45%.
- The groups differ in size. If ‘more widespread’ means a larger share of members, the claim is not justified.
6. 24/30 = 80% of those surveyed, not established as 80% of the school. The chess-club sample may favour chess.
- 24 ÷ 30 × 100 = 80%, so the sample calculation is correct.
- Students attending chess club are not a representative sample of all 300 students.
- Survey all students, or randomly select students across the school using the same neutral question. Report responses and non-responses; do not invent the result.
Mistakes worth catching
Treating visible cropped bar heights as full-value ratios.
Read the values and divide them. Check the baseline first.
Comparing raw counts when groups differ in size.
Calculate shares using each group's own total and label the comparison.
Turn your work into a next step
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Skills covered
Graphs, data and probability
- Identify how axis scales and comparison choices can mislead.
- Check a claim against the actual values and explain a fairer presentation.
Choose this practice by the skills you need. Grade placement and strand names vary between school systems; one worksheet covers selected skills rather than every expectation in a topic.
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