Evaluate data presentation
Check axis scales, denominators and symbol sizes before accepting a visual comparison.
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Before you begin
- Read an English passage closely
- Distinguish a statement from its supporting reason
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Before evaluating support, what should you identify?
What you will learn
- Identify misleading statistical presentation
- Explain the numerical effect of a presentation choice
Read numbers before the visual impression
A truncated vertical axis can make a modest change look enormous. Values 100 and 110 rise by 10%, but bars drawn from baseline 95 have displayed heights 5 and 15, a three-to-one ratio. The graph may communicate detail legitimately if its scale is clear, but its apparent bar ratio is not the ratio of the underlying counts.
Irregular axis intervals must be marked and interpreted correctly. A large gap between dates can distort the apparent speed of a trend if displayed with the same spacing as a short gap. Labels, units and denominators are essential evidence, not decoration.
Check area and comparable definitions
Doubling the width and height of a pictogram multiplies its area byfour, so it may exaggerate a doubling of counts. A fair area representation scales linear dimensions by the square root of the count ratio. Percentages must use comparable populations and periods.
Distinguish a percentage-point increase from a relative percentage change. Moving from 40% to 50% is 10 percentage points and 25% relative to 40%. Describe the distortion and its effect rather than merely calling a graph ‘biased’.
Sources for this lesson
Pause and explain
An increase from 40% to 50% is how many percentage points?
Worked example
Compare counts 100 and 110 when bars start at 95.
Show the worked solution
- Actual change is 10/100=10%.
- Displayed heights are 5 and 15.
- The displayed ratio 3 does not equal the count ratio 1.1.
Answer The count rises by 10%, although the truncated bars appear three times as high. The baseline must be considered before interpreting the visual size difference.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Guided: Calculate the actual relative increase from 100 to 110.
Give me a hint
Divide the increase by the original count.
Compare my reasoning
- The difference is ten.
- Ten divided by one hundred is 0.1.
- Multiply by 100 for a percentage.
The relative increase is 10%. The truncated graph’s three-to-one displayed-height ratio is a different quantity and cannot replace this calculation.
Look for these in your work
- Finds the difference
- Uses the original denominator
- Separates display from data
Independent: A pictogram is twice as wide and twice as high for a count that doubles. Explain the problem.
Give me a hint
Compare areas.
Compare my reasoning
- Area scales by width×height.
- 2×2=4.
- The count ratio is only 2.
The larger pictogram occupies four times the area although the count only doubles. If viewers interpret area as quantity, the display exaggerates the increase; an area-based doubling needs a linear scale factor of√2.
Look for these in your work
- Calculates area scaling
- Compares the count ratio
- Explains the visual distortion
Application: Support rises from 40% to 50%. Report both the point change and relative percentage change.
Give me a hint
Use subtraction for points and the original value for relative change.
Compare my reasoning
- 50−40=10 percentage points.
- 10/40×100=25%.
- Label the two different measures.
Support increases by 10 percentage points, or 25% relative to its original 40% level. Calling it a 10% relative rise confuses the two measures.
Look for these in your work
- Finds the point change
- Finds the relative change
- Labels both
Common mistakes
- Using displayed height as a count ratio on a truncated axis
- Confusing area with length
- Confusing percentage points and percentages
What can you explain now?
An increase from 40% to 50% is how many percentage points?
Compare with the explanation
Ten percentage points
The difference is ten points; the relative change is 25%.
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An increase from 40% to 50% is how many percentage points?
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