The numbers can stay the same while the visual story changes dramatically.
Lesson 06 · StatisticsYour learning goal
Explain how graph format, scale, missing context and selective presentation can lead to misinterpretation.
Check what the lengths really represent
Bars normally communicate magnitude through length from a common zero baseline. If values are 96 and 100 but the axis begins at 90, the visible lengths are 6 and 10. A reader comparing those lengths may see a 66.7% increase, although the recorded value increases by approximately 4.17%. Read the axis before judging the size of a change.
A non-zero axis is not automatically deceptive
A restricted vertical range can make small fluctuations easier to study, especially on a line graph. The important questions are whether the range is clear, whether the graph type and context justify it, and whether the accompanying claim is supported. A labelled temperature line from 18°C to 22°C can be useful; it does not make 22°C twice as warm as 11°C.
Look for more than a truncated axis
Unequal intervals can distort slopes. Missing dates can hide an inconvenient period. A pictograph with symbols enlarged in two dimensions can exaggerate area. Three-dimensional effects can obscure sector proportions. Missing units, totals, sources or denominators can prevent fair interpretation. A misleading title can turn an accurate graph into an unsupported claim.
Critique the effect, not the designer’s motives
State the feature, explain how it changes interpretation and support your explanation with values. You can establish that a graph is misleading without claiming to know why its creator made it. A useful correction preserves the source data, chooses a suitable representation and restores the information readers need.
Explore · predict, test, explain
Change the scale, keep the evidence.
Same data. A different visual story.
The fixed data is Before: 96 units; After: 100 units. Change the minimum from 0 to 90 and compare the visible bar lengths with the actual values.
Line graphs use equally spaced positions here: use observations at equal time intervals. Do not use a line to connect unrelated categories. Circle graphs require a positive total.
Worked examples
Follow the reasoning.
The disappearing baseline
Two recorded values are 96 and 100.
On a zero-based graph, their lengths are in the ratio 100 ÷ 96, approximately 1.0417.
With a baseline of 90, the visible lengths have ratio 10 ÷ 6, approximately 1.6667.
The data has not changed. The drawn lengths can encourage an exaggerated comparison if the baseline is overlooked.
Twice as tall, four times the area
A square icon is 10 mm wide and 10 mm tall: its area is 100 mm².
Doubling width and height gives a 20 mm by 20 mm icon: 400 mm².
That is four times the area, not twice.
For twice the value, use two equal symbols or a bar with twice the length from zero.
Guided Practice
Build an explanation.
A line graph displays temperature from 18°C to 22°C. Is it necessarily misleading?
Give me a hint
Ask what the reader is trying to detect and whether the limits are visible.
Compare a worked response
No. A clearly labelled restricted scale can reveal small fluctuations. Critique a specific unsupported interpretation rather than declaring every non-zero axis wrong.
A graph shows January, February and December equally spaced and connects them. What needs checking?
Give me a hint
Compare the time gaps: one month and ten months.
Compare a worked response
If horizontal distance represents elapsed time, equal spacing distorts the timeline. Include the omitted months or use proportional spacing, and identify missing observations.
Independent Practice
Test the idea, then check your reasoning.
Feedback explains your chosen response. These activities are practice, not a school mark.
Connections
Use it beyond this page.
Use the Scale Manipulator. Keep 96 and 100 fixed while changing the minimum from 0 to 90. Explain why the visible bar-length ratio changes but the percentage change does not.
Take it further
Design two headlines for the same accurately labelled graph: one defensible and one overstated. Identify the exact words that make the second headline go beyond the evidence.