Scale Distortion Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Scale Distortion.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Scale distortion occurs when a graph's axis does not start at zero or uses inconsistent intervals, making small differences appear large or large differences appear small.

Zoom in on tiny differences to make them look huge, or zoom out to hide them.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Always check if y-axis starts at zero and if scale is linear.

Common stuck point: Always check where the y-axis starts — if it does not start at zero, ask whether the visual impression still matches the actual magnitude of differences.

Worked Examples

Example 1

easy
Two graphs show the same data (unemployment: 4% to 5%). Graph A: y-axis from 0–10%. Graph B: y-axis from 3.5%–5.5%. Describe what each graph communicates visually and which is more honest.

Solution

  1. 1
    Graph A (0–10%): the 1% increase looks small — the bar rises modestly from 40% to 50% of the axis height
  2. 2
    Graph B (3.5–5.5%): the same 1% increase looks enormous — the bar rises from near the bottom to near the top of the compressed axis
  3. 3
    True change: \frac{5-4}{4} \times 100 = 25\% relative increase — significant but not catastrophic
  4. 4
    Graph A is more honest for showing absolute magnitude; Graph B exaggerates relative change

Answer

Graph A (wider scale) shows true magnitude honestly; Graph B's compressed scale makes the change look much larger.
Scale selection dramatically affects visual impression. There is no universally 'right' scale, but starting at 0 for bar charts prevents area distortion. For line charts, the appropriate scale depends on the question being asked (absolute change vs. relative change).

Example 2

medium
A graph uses a logarithmic scale for a dataset ranging from 1 to 1,000,000. Explain when a log scale is appropriate vs. misleading, and how to label it correctly.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A pictograph shows a 2021 salary twice as large as a 2020 salary by doubling both the height AND width of a dollar bill icon. If the actual increase was 2×, by what factor does the icon area increase?

Example 2

hard
A company's revenue chart has an x-axis with uneven time intervals (2010, 2012, 2016, 2017, 2018). The line shows constant growth. Explain how uneven spacing creates scale distortion.
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Related Concepts

Misleading Graphs

Background Knowledge

These ideas may be useful before you work through the harder examples.

misleading graphs