Practice Scale Distortion in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick 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.

Showing a random 20 of 50 problems.

Example 1

easy
A y-axis starts at 20 instead of 0. Two bars read 22 and 26. What does the truncation do to the difference?

Example 2

hard
A pictogram shows revenue with stacks of coins. Company A has 5 coins; company B has 10. Each coin is the same size. Is this honest?

Example 3

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.

Example 4

medium
A chart maps value v to pixels as p=5(v−70). Two values are 80 and 90. Find the true and the displayed ratios.

Example 5

hard
A bar of true value v is shown with pixel height h(v)=k(v−b). For b>0 and v1=110, v2=100, the perceived ratio overstates the true ratio by what factor when b=90?

Example 6

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.

Example 7

easy
On a linear y-axis, the gap from 0 to 50 is 100 pixels. How many pixels is the gap from 50 to 100?

Example 8

medium
A scatterplot uses a log scale on BOTH axes and the points fall on a straight line. What kind of relationship does a straight line on a log-log plot indicate?

Example 9

medium
A bar chart shows two values 400 and 800 on a y-axis from 0 to 1000. The true ratio is 2. What is the pixel-height ratio?

Example 10

easy
A bar chart's y-axis is truncated to start at 90. True values are 92 and 96. What is the true percent difference?

Example 11

easy
A 3D bar chart uses tilted prisms instead of flat bars. How can this distort the reader's perception?

Example 12

hard
Two charts show the same data but on aspect ratios 4:1 and 1:4. Explain why the perceived 'volatility' of a line series differs even though the slopes are mathematically the same.

Example 13

challenge
A bar of true value v is drawn on a linear axis with baseline b<v, so pixel height h(v)=k(v−b). Prove that the perceived ratio h(v1)/h(v2) equals the true ratio v1/v2 if and only if b=0.

Example 14

easy
If a pictogram doubles BOTH the height and the width of an icon to represent a 2× change, by what factor does the icon's area grow?

Example 15

hard
A chart's y-axis is reversed (high values at the bottom). Stock prices rise on screen but the labels say they're falling. What category of distortion is this?

Example 16

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.

Example 17

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 18

medium
A linear chart maps value v to pixels by p=10v. A distorted version truncates the baseline to b=80: p′=10(v−80). For v1=90,v2=85, find the true height ratio and the distorted height ratio.

Example 19

challenge
On a log10 axis, the segment from value a to value b>a has the same pixel length anywhere on the axis as long as b/a is constant. A designer wants to make a 10% growth look as big as a doubling did on a linear chart. Explain why a log axis prevents this trick.

Example 20

hard
A truncated-axis chart starts at b. Show that the displayed ratio (v1−b)/(v2−b) overstates the true ratio v1/v2 whenever v1>v2>b>0.
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