“There are three kinds of lies: lies, damned lies and statistics.”

Misleading graphics

Line chart that looks flat
The same data with a rescaled axis: it looks like strong growth
The same data with a different axis range: it looks like a decline
The same decline without axis labels
Rolling average of the BIIB share price
Histogram of Titanic passengers
Titanic passenger histogram
Titanic passenger histogram, misleading version
Titanic passenger histogram, another misleading version
Size comparison, 2025 vs 2026
2025 2026

Misleading averages

The average net worth of a SpaceX employee is at least 63 million dollars.

Explanation

  • Elon Musk is a SpaceX employee.
  • Elon Musk's net worth is 636 billion dollars according to Forbes.
  • There are roughly 10,000 SpaceX employees.
  • Assuming everyone's net worth, aside from Elon Musk's, is 0 gives us a lower bound.
  • $$636\text{B} \div 10{,}000 \simeq 63\text{ million dollars per employee}$$
The Vatican has an average of two popes per square kilometre.

Explanation

  • The Vatican has an area of $0.49\text{ km}^2$.
  • There is one pope in the Vatican.
  • $1\text{ pope} \div 0.49\text{ km}^2 \simeq 2.04\text{ popes per km}^2$
You have an above-average number of arms.

Explanation

  • Most humans have two arms.
  • Some humans have fewer than two arms.
  • Therefore, the arithmetic mean number of arms per person is slightly below two.
  • If you have two arms, you are therefore slightly above average.

Misleading samples

8 out of 10 dentists recommend our toothpaste.

Selection bias

  • Which dentists were included in the survey?
  • How were they selected?
  • How many dentists were asked in total?
  • A sample can give a misleading result if it is not representative of the population.
Survivorship bias

Survivorship bias

  • We only observe the aircraft that successfully returned from combat.
  • The bullet holes show where an aircraft can be hit and still survive.
  • The missing data are the aircraft that were hit elsewhere and did not return.
  • Therefore, the areas with few bullet holes are the areas that should be reinforced.
No coin is fair and I can prove it.

Selective stopping

  • With a small sample, random fluctuations can make a fair coin look biased.
  • Keep flipping the coin until the results look sufficiently unusual.
  • If you stop only when the data support your claim, the sample is no longer neutral.
  • The stopping rule becomes part of the experiment and affects the conclusion.
Drinking water improves your luck at dice.

Regression to the mean

  • Suppose you start drinking water immediately after an unusually bad series of dice rolls.
  • Extreme results are usually followed by results closer to the average.
  • Your next rolls are therefore likely to improve even if the water has no effect.
  • The improvement can then be incorrectly attributed to drinking water.
Like people, data will admit to anything if you torture it long enough.

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