Numbers · 3 min read
Mean vs Median: Which Average Should You Trust?
Why the average salary is higher than what most people earn: the difference between mean and median, when each misleads, and which to use.
By the Cognosc team ·
Nine people in a bar earn around $40,000 a year. Then a billionaire walks in. The average income in the bar is now over $100 million. Nobody got richer except in the statistics.
That’s the difference between the mean and the median, and it matters every time you read about “average” pay, house prices or wealth.
Try it
One salary moves. What happens to the average?
Nine people’s pay. Slide the top earner’s salary up.
Median: $38,000. Mean: $144,000. One person’s pay moved; the mean ran off after them, while the median, the middle earner, didn’t budge. When a few values are huge, the median is closer to what’s typical.
Two kinds of average
The mean is what most people call the average: add everything up and divide by how many there are.
The median is the middle value: line everything up from smallest to largest and take the one in the middle. Half are below it, half above.
For many kinds of data, like heights, the two are nearly the same. They split apart when data is skewed: when a few values are far bigger (or smaller) than the rest.
Why the mean runs away
The mean uses the size of every value, so one huge value pulls it a long way. The median only cares about the order, so the billionaire counts as just one person above the middle, no matter how rich.
That’s why incomes, house prices and wealth are usually reported as medians. In most countries, the mean income is well above the median, because a small number of very high earners pull it up. Most people earn less than the “average”.
Which one should you use?
- Use the median for the typical case when the data is skewed: incomes, house prices, wealth, waiting times, city sizes.
- Use the mean when the total matters, or the data is roughly symmetrical. If you want to know how much a company pays its staff in total, or how much fuel a fleet uses, the mean is what you need.
- Look at both. A big gap between them is itself useful information: it tells you the data is lopsided.
The mode
There’s a third average: the mode, the most common value. It’s handy for categories, like the most popular shoe size or the most common answer, but less useful for measurements that rarely repeat exactly.
A trick to watch for
Because the mean and median can differ so much, whoever chooses which to report can shape the story. A company might quote the mean salary to look generous; a union might quote the median to show that most staff earn less. Both can be accurate. The honest move is to say which average you’re using, and why.
Try it
Slide the top earner’s salary above and watch the mean race off while the median stays put.
The free statistics test includes a question on skewed averages and nine other ideas that are easy to get backwards.