Start with the recap, study the fully worked examples, then use the practice problems to
check your understanding of Misleading Graphs.
This page combines explanation, solved examples, and follow-up practice so you can move
from recognition to confident problem-solving in Statistics.
Concept Recap
Misleading graphs are data visualizations that distort the truth through techniques like truncated axes, inconsistent scales, cherry-picked time ranges, or manipulated aspect ratios to create false impressions and lead viewers to wrong conclusions.
A bar that looks 3× taller might only represent 10% more data if the axis doesn't start at zero. It's like taking a photo from a weird angle to make someone look taller. The data is true, but the picture lies.
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:Misleading Graphs organizes data so the right pattern is visible without distorting the counts or scale.
Common stuck point:Students often know a procedure related to misleading graphs but skip the recognition step: Am I choosing or interpreting a display that matches the type of data and the question being asked? That leads to a calculation or graph that looks reasonable but answers a different question.
Sense of Study hint:Ask: Am I choosing or interpreting a display that matches the type of data and the question being asked?
Worked Examples
Example 1
medium
A graph titled 'sales soaring' shows the y-axis from 980 to 1000, with bars at 990 and 995. Compute the actual percent change and explain the trick.
Answer
≈0.5%
First step
1
Change =995−990=5.
See the full worked solution + why-it-works coaching
Setup·Key insight·Why it works·Common pitfall·Connection
A truncated bar chart shows bar A reaching 80 pixels and bar B reaching 40 pixels, but the axis starts at 90. Bar A's true value is 100. What is bar B's true value?Axis starts at 90. Bar A = 100 (80 px visible). Bar B is 40 px — what is its true value?
Example 3
hard
A bar chart shows two bars with visible heights 30 and 60 pixels, axis truncated to start at 50. Bar A's true value is 80. What is bar B's true value, and what is the true ratio B:A?Axis starts at 50. Bar A = 80 (30 px). Bar B = 60 px visible — find the true value. Answer: 110, ratio B:A = 11:8.
Example 4
challenge
A chart claims revenue 'tripled' over 5 years. True values: year 1 = $80M, year 5 = $120M. Compute the true growth factor and the chart's exaggeration ratio.Revenue grew from $80M to $120M — factor 1.5, not the claimed 3× (exaggeration ratio = 2).
Example 5
easy
A bar graph shows Company A's sales at 100 and Company B's sales at 110, but the y-axis starts at 95 instead of 0. How does this make the graph misleading?
Example 6
medium
A pictograph compares two companies' profits. Company X uses a small money bag symbol and Company Y uses a money bag symbol that is twice as tall AND twice as wide (so 4 times the area). Company Y's profit is actually only twice Company X's. How is this misleading?
Practice Problems
Try these problems on your own first, then open the solution to compare your method.
Example 1
easy
A bar chart's y-axis starts at 90 instead of 0. Bar A reaches 92, bar B reaches 96. By the TRUE values, what is the actual difference?Y-axis starts at 90 — the bars look very different but the true difference is only 4.
Example 2
easy
A graph's y-axis starts at 50. Why might this be misleading when comparing two bars at 52 and 54?Y-axis starts at 50 — a 2-unit gap appears huge due to truncation.
Example 3
easy
A pictograph uses one icon = 10 cars, but draws bigger icons for one company to look better. What feature is being manipulated?
Example 4
easy
A line graph only shows data from a 2-week dip during a year of steady growth, labeled 'sales falling.' What technique is this?
Example 5
easy
A bar from 0 to 10 sits next to a bar from 0 to 12 on a proper zero-baseline axis. By how much percent is the second taller?Zero baseline: Bar B is 20% taller than Bar A (12 vs 10).
Example 6
easy
A graph uses uneven spacing on the time axis: 2000, 2005, 2006, 2020. What problem does uneven spacing cause?The gap from 2005 to 2006 (1 year) takes the same space as 2006 to 2020 (14 years) — distorting the apparent rate of change.
Example 7
easy
A truncated-axis bar chart makes bar B look 3 times taller than bar A, but A = 100 and B = 120. What is the TRUE ratio of B to A?Honest zero-baseline chart: true ratio B/A = 120/100 = 1.2, not the 3× suggested by a truncated axis.
Example 8
easy
To fairly compare quantities with a bar chart, where should the vertical axis start?
Example 9
medium
A bar chart with axis starting at 80 shows bar A at 82 and bar B at 86. The visible heights are 2 units vs 6 units. What is the ratio of visible heights, and the ratio of true values?Axis starts at 80: visible heights are 2 vs 6 (ratio 3), but true values 82 vs 86 give ratio ≈ 1.05.
Example 10
medium
A 3D pie chart tilts so a front slice looks bigger. The slice is truly 20% of the data. How many degrees should it actually be?
Example 11
medium
Company X reports '50% growth!' on a chart, but profit went from 2to3. Is the 50% claim numerically correct, and is the chart's huge bar jump misleading?Honest zero-baseline chart: profit rose from $2 to $3 — a true 50% increase on a tiny base.
Example 12
medium
A line graph compresses the y-axis (each unit = many values) to flatten a steep rise. The data rose from 100 to 300 over a year. What is the true percent increase?Data rose from 100 to 300 — a 200% true increase that a compressed y-axis would make look flat.
Example 13
medium
A bar chart with a baseline at 95 shows test averages: School A 96, School B 98, School C 100. By true values, how much higher is C than A, and what percent of A is that?Baseline at 95: C looks far ahead of A, but the true gap is only 4 points (≈ 4.2% of A).
Example 14
medium
An area graph doubles both width and height of an icon to show 'twice the value.' By how many times does the AREA actually grow?
Example 15
medium
A graph shows monthly data but skips the months where sales dropped, plotting only rising months connected by a line. What two techniques combine here?
Example 16
medium
A bar chart truncated at 40 makes B look double A. Truth: A = 44, B = 48. If redrawn from 0, what is B's bar height as a percent of A's?Baseline at 40 makes B appear ~2× A; from zero, B is only ≈109% of A.
Example 17
medium
A dual-axis chart plots revenue (left axis 0-100) and complaints (right axis 0-5) so their lines cross dramatically. Is the crossing meaningful?
Example 18
challenge
A bar chart truncated at value t makes A = 60 appear half as tall as B = 80 (visible heights in ratio 1:2). Find t.Baseline t = 40: visible heights are 20 and 40 (ratio 1:2), matching the deceptive setup.
Example 19
challenge
A pictograph claims each coin = 100.Toshow250, a designer scales one coin to 2.5x its width AND height. The reader perceives value by area. What value does the area suggest?
Example 20
challenge
A line graph of yearly profit (in \$1000s): 2018=50, 2019=52, 2020=51, 2021=90. A headline says 'profit nearly doubled.' Over which single year is that true, and what is the true overall change from 2018 to 2021?Only the 2020→2021 jump is near-doubling; the overall 2018→2021 change is +80%, not +100%.
Example 21
easy
A bar chart's y-axis starts at 40 instead of 0. Bar A reaches 45, Bar B reaches 50. What is the true difference between B and A?Y-axis starts at 40: the 5-unit true difference (50 − 45) appears exaggerated visually.
Example 22
easy
A pictograph uses one icon =5 books. Brand A draws icons that are twice as wide AND twice as tall as Brand B's. Why is this misleading?
Example 23
easy
A news story shows a line chart of stock prices for just the worst week of the year and titles it 'Stock collapses.' What technique is being used?
Example 24
easy
A bar chart with a proper zero baseline shows Bar A at 40 and Bar B at 50. By what percent is Bar B taller?Zero baseline: Bar B (50) is 25% taller than Bar A (40).
Example 25
easy
A line graph plots years 2010,2011,2015,2016 on the x-axis evenly spaced. What is the problem?The 2011→2015 gap (4 years) is drawn the same width as the 1-year gaps — distorting the apparent rate of change.
Example 26
easy
Bar A reaches 100 and Bar B reaches 103, but the y-axis starts at 99. What is the true percent increase from A to B?Y-axis starts at 99: a true 3% increase (100 → 103) looks like a near-doubling.
Example 27
medium
A bar chart's y-axis starts at 200. Visible heights of bars A and B are 20 and 40 pixels (ratio 1:2). True values are 220 and 240. What is the TRUE ratio of B to A?Axis starts at 200: visible heights are 20 vs 40 (ratio 1:2), but true ratio 240/220 ≈ 1.09.
Example 28
medium
A 3-D pie chart tilts so the front slice (truly 15% of data) looks bigger. How many degrees of the circle should that slice actually occupy?
Example 29
medium
A pictograph: 1 stick figure =100 people. School A shows 3 figures drawn at normal size; School B shows 4 figures drawn 1.5× as tall. True ratio of B's people to A's?
Example 30
medium
A line graph uses a logarithmic y-axis but the title says 'linear growth.' Why is the description misleading even if the chart is technically correct?
Example 31
medium
A dual-axis chart plots revenue (left axis, 0-100) and complaints (right axis, 0-10) so the lines cross. Why is the apparent 'correlation' suspect?
Example 32
medium
A bar chart compares city populations using bubbles whose DIAMETERS scale with population. City X has population 4 million, city Y has 1 million. By how many times does X's BUBBLE AREA look bigger than Y's?
Example 33
medium
A line graph drops a key data point that breaks the trend. What is this trick called?
Example 34
medium
A bar chart's y-axis goes upward from 100 at the top to 0 at the bottom (inverted). Sales of 80 appear higher on the page than sales of 20. Why is this misleading?
Example 35
hard
A chart claims '200% growth' when sales went from 10 to 20. Is the claim correct, and what is the actual percent increase?Sales went from 10 to 20 — that is a 100% increase (doubling), not the claimed 200%.
Example 36
hard
A poll graph reports '60% support' but interviewed only members of one political party. What kind of misleading data display is this?
Example 37
hard
A line chart of monthly revenue uses different y-scales each month (recomputed to fit). Why is this misleading?
Example 38
hard
A truncated bar chart shows bar B looking 4× as tall as bar A. True values: A=50, B=55. What is the true percent increase, and what visual percent does the chart suggest (assume the eye reads height ratio)?
Example 39
hard
A scatterplot drawn on a tiny range of x makes two variables look uncorrelated. Zooming out shows a clear positive trend. What chart trick is operating?
Example 40
medium
A line graph shows monthly website visits over a year, but the x-axis is not evenly spaced — January to June are compressed into a small space while July to December are spread out. How could this affect the interpretation?
Example 41
hard
A politician presents a pie chart showing their party received 45% of votes, but the 3D perspective makes their slice appear to take up more than half the chart. Identify all the misleading techniques and explain how to fix the chart.