Numbers That Lie

Ten people in a bar, each earning $50k. A billionaire walks in — average income is now ~$91 million; the median (the middle person) is still $50k. Any quantity with extreme values — income, house prices, company salaries, wait times — has an average that follows the outliers and a median that follows the people. Whoever chooses which one to show you is making an argument, not reporting a fact.

incomes: 50k ×10, then +1 billionaire

average:  $91,000,000   "a prosperous establishment!"
median:   $50,000       what the typical person earns

# where you'll meet this trick:
"average salary at our company is $145k"   ← founders' equity
"average home price rose 12%"              ← luxury sales spike
"average customer saves $400"              ← three whales

# the defusing question: "what's the MEDIAN?"
# if they won't say, that's your answer.

A disease affects 1 in 1,000 people. A test is 99% accurate. You test positive — how worried should you be? Most people (including many doctors, in studies) say 99%. The real answer is about 9%. The rare thing stays rare even after a positive signal — because the 1% error rate operates on the huge healthy population, false alarms outnumber real cases ten to one.

100,000 people · disease rate 1/1,000 · test 99% accurate

actually sick:      100 → ~99 true positives
actually healthy: 99,900 → ~999 FALSE positives  ← ten times more!

positive tests: 1,098 · actually sick: 99 → ~9%

# the same math runs: fraud alerts, security scanners,
# hiring "signals", medical screenings, spam filters.
# defusing question: "how common is this thing BEFORE the test?"

WWII: analysts mapped bullet holes on returning bombers and proposed armoring the most-hit spots. Statistician Abraham Wald flipped it: armor where returning planes weren't hit — planes hit there never made it home. The data was honest; the dataset was missing its most important members. You only ever hear from survivors.

# the modern reruns:
"college dropouts become billionaires"   ← the million broke
                                            dropouts don't give TED talks
"this 100-year-old smoked daily"         ← the dead smokers
                                            aren't interviewed
"every successful founder works 90h"     ← the burned-out 90h
                                            failures are invisible
"our alumni earn $200k"                  ← alumni who answer
                                            surveys ≠ all alumni

# the defusing question:
# "who ISN'T in this dataset — and why not?"

Ice cream sales and drowning deaths rise together every year. Ice cream doesn't drown people — summer causes both. When A and B move together there are always four suspects: A→B, B→A (reverse!), hidden C→both (the confounder), or pure coincidence (with enough variables, some correlate by luck). Headlines pick the story that sells; your job is to line up all four.

"kids who eat breakfast get better grades"
  A→B?  breakfast fuels brains          (the headline)
  B→A?  unlikely here
  C→AB? stable households produce both
        breakfast AND homework help     (the boring truth?)
  luck? with 500 diet variables studied, some hit

# reverse causation, the underrated one:
"CEOs who exercise run better companies"
  or: people whose companies run well have time to exercise

# defusing question: "what ELSE could produce both?"

The favorite trick of scary headlines: relative change sounds huge when the absolute risk is tiny. "Bacon raises bowel cancer risk 18%!" — from about 5% lifetime risk to about 6%. One percentage point, for a lifetime of sandwiches; your call, but make it on the real numbers. Also in this family: percent vs percentage points, and the asymmetry of losses (−50% then +50% ≠ back to even).

"18% increased risk!"      relative — sells papers
5% → 5.9%                  absolute — informs decisions

"interest rose from 4% to 6%"
= 2 percentage points, but "a 50% increase in rates"
# same fact, two headlines, pick your panic

# the down-up asymmetry:
$100 −50% → $50 +50% → $75, not $100
# a 50% loss needs a +100% gain to recover.
# (see Money Basics for what this does to portfolios)

# defusing question: "from WHAT, to WHAT, in absolute terms?"

Small groups produce extreme results by default — a hospital with 8 births will hit "75% boys this month" routinely; a hospital with 800 births never will. The counties with the highest cancer rates in America are rural and tiny… and so are the counties with the lowest rates. Small n doesn't just weaken a claim; it manufactures dramatic ones.

flip 5 coins  → 4+ heads happens ~19% of the time  (routine)
flip 500 coins → 400+ heads happens ~never          (call a physicist)

# where it bites:
"9 of 10 dentists agree"        which 10? of how many asked?
"our A/B test won! (n=40)"      re-run it. n=40 "wins" constantly
5-star app with 6 ratings       vs 4.4 stars with 80,000

# defusing question: "what's the n?" — ask it EVERY time
# a percentage is quoted without a count.

A chart can mislead without a single false number. The classic: truncate the y-axis so it starts at 96 instead of 0, and a 2% difference towers like a cliff. The supporting cast: cherry-picked time windows ("since March!"), dual axes tuned to force a crossover, and 3D pie charts where the nearest slice looks biggest. The numbers are honest; the geometry isn't.

# same data: sales 96 → 98

y-axis 0–100:   ▁▁  "basically flat" (true)
y-axis 96–98:   ▁█  "EXPLOSIVE GROWTH" (also "true")

# the time-window cherry-pick:
"up 40% since March!"   ← and what happened in February,
                           that March was chosen as the start?

# defusing habits: read the axis numbers FIRST ·
# widen the window · treat 3D charts as decoration

Extreme results are part luck, and luck doesn't repeat — so extremes drift back toward normal on their own. The rookie of the year "slumps" (he was never that good). The worst-performing branch "turns around" after a manager visit (it was never that bad). This trap is cruel because it rewards punishment and mocks praise: scold after a terrible result and things improve (they would have anyway); praise after a great one and things decline (ditto). Flight instructors concluded exactly this — Kahneman built half a career on the observation.

extreme result = skill + luck
next result    = skill + fresh luck (average) → less extreme

# the illusions it creates:
"the intervention worked!"    ← applied at the worst moment;
                                 bounce-back was free
"the magazine-cover jinx"     ← covers select peak-luck moments
"my slump ended when I
 changed my shoes"            ← it ended because slumps end

# defusing question: "compared to what — and would it
# have bounced back anyway?" (that's why trials have
# control groups.)

One question per trap. Ask them out loud in meetings; watch presentations improve.

average quoted?      → "what's the median?"
detector praised?    → "how rare is the thing it detects?"
success pattern?     → "who isn't in this dataset?"
A causes B?          → "what else could produce both?"
scary percentage?    → "from what, to what, absolutely?"
impressive rate?     → "what's the n?"
dramatic chart?      → "where does the y-axis start?"
before/after story?  → "would it have bounced back anyway?"

This pairs naturally with Money Basics (percentage games with your savings), Mental Math (estimate first — absurd numbers announce themselves), and Learning (the fluency illusion is a self-inflicted statistics error).