11-15-2025, 05:16 PM
Chapter 16 — Misleading Graphs & Statistics
Statistics is powerful — but it can also be manipulated.
Graphs and numbers can easily be presented in a way that looks correct but gives a false impression.
This chapter teaches you how to spot the tricks.
---
16.1 Trick #1 — Starting the Axis Above Zero
One of the most common ways to mislead people.
Example:
A graph comparing two values:
• Product A: 51
• Product B: 50
If the y-axis starts at 49:
The bars look dramatically different — even though the real difference is tiny.
Honest graphs start the axis at 0.
---
16.2 Trick #2 — Stretching or Squashing the Scale
If you compress the vertical axis:
• the graph looks stable
If you stretch the vertical axis:
• small changes look dramatic
Advertisers, news headlines, and political graphs use this constantly.
---
16.3 Trick #3 — Misleading Pie Charts
Common tricks:
• slices not proportional
• 3D pie charts making slices appear larger
• colours used to exaggerate importance
• reordering slices to create false emphasis
Pie charts should always be checked carefully.
---
16.4 Trick #4 — Missing Information
Sometimes a statistic is technically correct but missing critical context.
Examples:
• “Crime doubled!” → from 1 incident to 2
• “Sales increased 200%” → from £10 to £30
• “95% agree” → only 20 people surveyed
Always ask:
“Out of how many?”
---
16.5 Trick #5 — Biased Sampling
If the sample is biased, the results are worthless.
Examples:
• asking only your friends
• online polls (self-selected)
• surveys done in specific locations
• tiny sample sizes
Example:
“90% of people prefer Product X”
(…but only 10 people were questioned)
Always ask:
“Was the sample random and large enough?”
---
16.6 Trick #6 — Cherry-Picking Data
Choosing only the data that supports your argument.
Example:
A company reports profits for the last 3 months (all good)
but hides the previous 9 months (all bad).
Cherry-picking is extremely common in:
• politics
• marketing
• media
• scientific misinformation
---
16.7 Trick #7 — Using Averages to Hide the Truth
Example:
Average income in a town = £50,000
But:
• one millionaire
• many people earning £20,000
The mean is misleading.
Median income may tell a completely different story.
Always check which average is used.
Mean vs Median:
• Mean is distorted by extreme values
• Median shows the “middle” real value
---
16.8 Trick #8 — Correlation vs Causation
Two things might happen at the same time —
but that doesn’t mean one causes the other.
Examples:
• Ice cream sales and drowning deaths both increase in summer
• Shoe size and reading skill both increase with age
• Rainfall and arcade ticket sales may match by coincidence
Correlation NEVER proves causation.
---
16.9 Trick #9 — P-hacking (advanced idea, simple meaning)
Researchers test MANY hypotheses, but only report the ones with “significant” results.
This creates false findings.
Signs of p-hacking:
• many minor variables tested
• only the successful ones reported
• tiny sample sizes
• dramatic claims based on weak evidence
---
16.10 Trick #10 — Unclear Units or Labels
Examples:
• “COVID cases doubled” (but from what?)
• “Sales increased” (over which time period?)
• “Traffic down 30%” (compared to last month or last year?)
Graphs can hide vital context using:
• no axis titles
• unclear scales
• missing units
Always demand clarity.
---
16.11 How to Read a Graph Like a Scientist
When you see a graph, ask:
1. Does the axis start at 0?
2. Is the scale stretched or compressed?
3. Are the slices proportional (pie charts)?
4. Is any data missing?
5. How big was the sample?
6. Which average is being used?
7. Are they confusing correlation and causation?
8. Are units clearly labelled?
9. Is the graph designed to persuade rather than inform?
This checklist protects you from misinformation.
---
16.12 Exam-Style Questions
1. A bar chart shows two values:
A = 45
B = 44
But the axis starts at 40.
Explain why this is misleading.
2. A survey reports “80% of customers are satisfied,”
but only 10 customers responded.
What is wrong here?
3. A pie chart is drawn in 3D.
Explain how this can distort perception.
4. A company shows sales for only the last 3 months.
Why might this be misleading?
5. Give an example where correlation does NOT imply causation.
---
16.13 Chapter Summary
• Graphs can easily manipulate perception
• Axis tricks exaggerate or hide differences
• Pie charts can be misleading
• Biased samples make results worthless
• Missing context is a major method of deception
• Mean, median, and mode can be used dishonestly
• Correlation does not mean causation
• Always read graphs critically
By spotting these tricks, you become immune to statistical misinformation —
a *superpower* in today’s world.
---
Written and Compiled by Lee Johnston — Founder of The Lumin Archive
Statistics is powerful — but it can also be manipulated.
Graphs and numbers can easily be presented in a way that looks correct but gives a false impression.
This chapter teaches you how to spot the tricks.
---
16.1 Trick #1 — Starting the Axis Above Zero
One of the most common ways to mislead people.
Example:
A graph comparing two values:
• Product A: 51
• Product B: 50
If the y-axis starts at 49:
The bars look dramatically different — even though the real difference is tiny.
Honest graphs start the axis at 0.
---
16.2 Trick #2 — Stretching or Squashing the Scale
If you compress the vertical axis:
• the graph looks stable
If you stretch the vertical axis:
• small changes look dramatic
Advertisers, news headlines, and political graphs use this constantly.
---
16.3 Trick #3 — Misleading Pie Charts
Common tricks:
• slices not proportional
• 3D pie charts making slices appear larger
• colours used to exaggerate importance
• reordering slices to create false emphasis
Pie charts should always be checked carefully.
---
16.4 Trick #4 — Missing Information
Sometimes a statistic is technically correct but missing critical context.
Examples:
• “Crime doubled!” → from 1 incident to 2
• “Sales increased 200%” → from £10 to £30
• “95% agree” → only 20 people surveyed
Always ask:
“Out of how many?”
---
16.5 Trick #5 — Biased Sampling
If the sample is biased, the results are worthless.
Examples:
• asking only your friends
• online polls (self-selected)
• surveys done in specific locations
• tiny sample sizes
Example:
“90% of people prefer Product X”
(…but only 10 people were questioned)
Always ask:
“Was the sample random and large enough?”
---
16.6 Trick #6 — Cherry-Picking Data
Choosing only the data that supports your argument.
Example:
A company reports profits for the last 3 months (all good)
but hides the previous 9 months (all bad).
Cherry-picking is extremely common in:
• politics
• marketing
• media
• scientific misinformation
---
16.7 Trick #7 — Using Averages to Hide the Truth
Example:
Average income in a town = £50,000
But:
• one millionaire
• many people earning £20,000
The mean is misleading.
Median income may tell a completely different story.
Always check which average is used.
Mean vs Median:
• Mean is distorted by extreme values
• Median shows the “middle” real value
---
16.8 Trick #8 — Correlation vs Causation
Two things might happen at the same time —
but that doesn’t mean one causes the other.
Examples:
• Ice cream sales and drowning deaths both increase in summer
• Shoe size and reading skill both increase with age
• Rainfall and arcade ticket sales may match by coincidence
Correlation NEVER proves causation.
---
16.9 Trick #9 — P-hacking (advanced idea, simple meaning)
Researchers test MANY hypotheses, but only report the ones with “significant” results.
This creates false findings.
Signs of p-hacking:
• many minor variables tested
• only the successful ones reported
• tiny sample sizes
• dramatic claims based on weak evidence
---
16.10 Trick #10 — Unclear Units or Labels
Examples:
• “COVID cases doubled” (but from what?)
• “Sales increased” (over which time period?)
• “Traffic down 30%” (compared to last month or last year?)
Graphs can hide vital context using:
• no axis titles
• unclear scales
• missing units
Always demand clarity.
---
16.11 How to Read a Graph Like a Scientist
When you see a graph, ask:
1. Does the axis start at 0?
2. Is the scale stretched or compressed?
3. Are the slices proportional (pie charts)?
4. Is any data missing?
5. How big was the sample?
6. Which average is being used?
7. Are they confusing correlation and causation?
8. Are units clearly labelled?
9. Is the graph designed to persuade rather than inform?
This checklist protects you from misinformation.
---
16.12 Exam-Style Questions
1. A bar chart shows two values:
A = 45
B = 44
But the axis starts at 40.
Explain why this is misleading.
2. A survey reports “80% of customers are satisfied,”
but only 10 customers responded.
What is wrong here?
3. A pie chart is drawn in 3D.
Explain how this can distort perception.
4. A company shows sales for only the last 3 months.
Why might this be misleading?
5. Give an example where correlation does NOT imply causation.
---
16.13 Chapter Summary
• Graphs can easily manipulate perception
• Axis tricks exaggerate or hide differences
• Pie charts can be misleading
• Biased samples make results worthless
• Missing context is a major method of deception
• Mean, median, and mode can be used dishonestly
• Correlation does not mean causation
• Always read graphs critically
By spotting these tricks, you become immune to statistical misinformation —
a *superpower* in today’s world.
---
Written and Compiled by Lee Johnston — Founder of The Lumin Archive