x̄Mean, Median & Mode Lab

The 'average salary' that nobody actually earns.

Nine employees earn $30k; the CEO earns $3M. What's this company's 'average salary'?

Three spokespeople summarizing the same data differently.

Feel the why in three minutesFullscreen

Experiment

Hands-on experiment

Predict first — nine employees earn $30k; the CEO earns $3M. The company's average salary is…?

Move the CEO's salary (the 9 employees stay at $30k)

CEO salary$30M

9 employees ($30k) CEO Mean = balance point Median = middle of the ranksx-axis: $0 → $100M

Drag the slider. Only the CEO's dot and the mean's fulcrum get pulled right — the median line stays nailed in place.

Mean salary

$3.27M

Median salary

$3,000k

Read more — why it exists · insights · common mistakes · formulasExpand ▾

Why

Why does this exist?

'The average salary', 'the average home price', 'average life expectancy' — the world summarizes groups into single numbers. And that number often feels wrong compared to your reality.

Because there's more than one way to summarize. Add-and-divide (mean), line-up-and-pick-the-middle (median), most-common-value (mode) — the three can produce wildly different numbers from the same data.

Especially in top-skewed distributions like income and wealth, the mean gets dragged by a handful of extremes. The habit of checking which spokesperson is talking — that's the first step to not being fooled by news and statistics.

Insight

Insights from the video

“The mean isn't democratic — one big number dominates the vote.”
In a mean, every value participates in proportion to its size. The CEO's $3M speaks louder than a hundred employees combined. The median is one-person-one-vote.

“The question chooses the spokesperson.”
'Total payroll budget?' — the mean. 'A typical employee's life?' — the median. 'The most common case?' — the mode. Choosing a representative isn't taste; it's a function of the question.

Misconception

Common misconceptions

Half the people earn above average and half below.

✓

That's the median's property. The mean gets dragged by extremes, so in skewed distributions like salaries, most people can be 'below average'.

One representative number is enough — the mean IS the group.

✓

Every summary throws information away. Depending on what got discarded (skew, outliers, spread), some spokesperson will sound like a liar. Picking the representative that fits the question is where statistical literacy begins.

Formula

Writing it as math

Meet the three spokespeople, in formulas.

The mean

Add everything, divide by the count. Every value participates by its size, so it's sensitive to extremes — the same principle as a center of mass.

The median

Line up and take the middle. It sees only rank, not size, so the CEO earning $3M or $300M moves it not at all.

The mode

The majority's representative. Like 'the most common shoe size', it tells you the case you'll actually meet most often.

In Real Life

Where you meet it in real life

Salary and housing statistics

Why governments publish both mean and median — the gap between them is itself information: the size of the skew.

A shoe store's inventory

Order for the average size 9.4 and you go broke. Inventory follows the mode — the best-selling size.

The illusion in game revenue

Average spend per user is dragged up by a few 'whales'. To know the typical player, look at the median (usually $0).

The life-expectancy trap

The historical 'average lifespan of 40' was dragged down by infant mortality. Adults back then often lived to 60–70.

Try Yourself

Test yourself

Q1For the data [1, 2, 2, 3, 100], what are the mean and the median?Show answer ▾

Mean 21.6, median 2. One 100 dragged the mean up over tenfold while the median didn't budge — the difference in outlier resistance.

Q2The class average is 70. Can fewer than half the students score 70 or above?Show answer ▾

Yes — a few very high scores can pull the mean up. The 'half above, half below' property belongs to the median, not the mean.

Q3A headline reads 'Half the nation earns below the average income'. Is that strange?Show answer ▾

Not at all — with a top-skewed income distribution it's natural. In fact 'half earn below the MEDIAN' is always true, hence not news. Distinguish mean from median and the headline's identity shows itself.

Try answering yourself before revealing it — getting it wrong is where learning starts.

Connection