Practice Misleading Graphs in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
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
challengeDesign 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
mediumA school reports test scores per teacher but omits class sizes. Teacher A: mean from students. Teacher B: mean from students. Why is a bar chart of just the means misleading?
Example 3
mediumA 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
mediumA dual-axis chart plots revenue (left axis –) and complaints (right axis –) so the two lines cross. Why can this falsely suggest correlation?
Example 5
easyA chart compares 'total crime' in two cities of very different population using raw counts. What is the flaw?
Example 6
mediumA truncated-axis chart shows bars at heights and pixels above baseline . The true values are and . Find .
Example 7
mediumA dual-axis chart shows ice-cream sales (left axis, to ) and shark attacks (right axis, to ) tracking each other. Does the visual correlation prove causation?
Example 8
easyA pictogram doubles both the height AND width of an icon to show a value that doubled. What is wrong?
Example 9
easyA graph claims 'unemployment doubled' going from to . What technique makes the claim feel dramatic?
Example 10
mediumA 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 income A. What visual area ratio results if both width and height scale by ?
Example 11
easyA pie chart shows , , . The artist colors the slice in a dim gray and the two slices in bright yellow. Is the chart numerically misleading?
Example 12
easyA line graph shows only the months where sales rose, omitting the months they fell. What technique is this?
Example 13
easyA bar chart's y-axis starts at instead of . What visual effect does this create?
Example 14
hardA pictogram shows three-dimensional spheres whose volumes are meant to represent the values . To be honest by volume, what is the ratio of the displayed radii?
Example 15
easyHonest bar chart: Brand A sells units, Brand B sells units, y-axis starts at . By roughly what percent is B greater than A? And how does this look on the chart?
Example 16
hardA chart claims 'support fell from to — a major collapse.' The y-axis runs to and bars sit at heights and . Compute the visual ratio, the true percentage-point drop, and the true relative drop.
Example 17
mediumA pictogram represents population by stick figures of height and width . To honestly show double the population using a figure twice as tall, what must the width do?
Example 18
challengeA bar chart truncates its y-axis to start at value . Two bars have true values . Show that the ratio of drawn pixel heights is and explain why choosing close to makes the exaggeration unbounded.
Example 19
mediumA 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
mediumA pictogram doubles a square icon's side from cm to cm to represent a increase. Compute the area ratio and explain what the honest scaling would be.