Practice Misleading Graphs in Math

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

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Quick Recap

A misleading graph is a data visualization that distorts the true pattern through truncated axes, unequal intervals, cherry-picked data, or manipulated scales.

A graph can tell any story the creator wants by choosing which data to show, where to start the axis, and how to scale the bars — visual clarity requires honest design.

Showing a random 20 of 50 problems.

Example 1

challenge
Design a single honest bar chart, then list the THREE independent edits that would each separately make it misleading without changing any underlying value. Name them.

Example 2

medium
A school reports test scores per teacher but omits class sizes. Teacher A: mean 80 from 4 students. Teacher B: mean 78 from 40 students. Why is a bar chart of just the means misleading?

Example 3

medium
A graph's bars are colored so the disliked option is bright red and the favored one is calm green, but axes are correct. Is this a data distortion?

Example 4

medium
A dual-axis chart plots revenue (left axis 0–100) and complaints (right axis 0–10) so the two lines cross. Why can this falsely suggest correlation?

Example 5

easy
A chart compares 'total crime' in two cities of very different population using raw counts. What is the flaw?

Example 6

medium
A truncated-axis chart shows bars at heights 20 and 80 pixels above baseline b. The true values are 60 and 120. Find b.

Example 7

medium
A dual-axis chart shows ice-cream sales (left axis, 0 to 100) and shark attacks (right axis, 0 to 5) tracking each other. Does the visual correlation prove causation?

Example 8

easy
A pictogram doubles both the height AND width of an icon to show a value that doubled. What is wrong?

Example 9

easy
A graph claims 'unemployment doubled' going from 4.0% to 4.1%. What technique makes the claim feel dramatic?

Example 10

medium
A magazine shows incomes as stacked coins where coin stack height is proportional to income, but the coin diameter also grows with the stack. Income B is 3× income A. What visual area ratio results if both width and height scale by 3?

Example 11

easy
A pie chart shows 30%, 30%, 40%. The artist colors the 40% slice in a dim gray and the two 30% slices in bright yellow. Is the chart numerically misleading?

Example 12

easy
A line graph shows only the months where sales rose, omitting the months they fell. What technique is this?

Example 13

easy
A bar chart's y-axis starts at 90 instead of 0. What visual effect does this create?

Example 14

hard
A pictogram shows three-dimensional spheres whose volumes are meant to represent the values 1,8,27. To be honest by volume, what is the ratio of the displayed radii?

Example 15

easy
Honest bar chart: Brand A sells 200 units, Brand B sells 250 units, y-axis starts at 0. By roughly what percent is B greater than A? And how does this look on the chart?

Example 16

hard
A chart claims 'support fell from 80% to 76% — a major collapse.' The y-axis runs 75% to 80% and bars sit at heights 5 and 1. Compute the visual ratio, the true percentage-point drop, and the true relative drop.

Example 17

medium
A pictogram represents population by stick figures of height h and width w. To honestly show double the population using a figure twice as tall, what must the width do?

Example 18

challenge
A bar chart truncates its y-axis to start at value b. Two bars have true values v1>v2>b. Show that the ratio of drawn pixel heights is v1−bv2−b and explain why choosing b close to v2 makes the exaggeration unbounded.

Example 19

medium
A graph shows 'cases of disease over time' with no y-axis label or values. The line goes up sharply. List three questions you should ask before drawing conclusions from this graph.

Example 20

medium
A pictogram doubles a square icon's side from 1 cm to 2 cm to represent a 2× increase. Compute the area ratio and explain what the honest scaling would be.
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