Mean vs. median: what’s the difference?
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 once you line everything up in order. Most of the time they land close together. When a few numbers are much bigger or smaller than the rest, the mean gets dragged toward them and the median barely moves. That’s when the median is the more honest number.
How to find each one
For the mean, add up every value and divide by how many there are. The mean of 2, 3 and 10 is 15 divided by 3, which is 5.
For the median, sort the values and take the one in the middle. The median of 2, 3 and 10 is 3. With an even count there are two middle values, so you take the point halfway between them: the median of 2, 3, 5 and 10 is 4.
Why they split apart
The mean uses how big every value is. The median only cares about order. So one huge number moves the mean a lot and the median hardly at all.
Try it below. Ten adults are eating lunch, earning between $31,000 and $94,000 a year. Then a billionaire walks in.
Dre pictures ten adults eating lunch in the school cafeteria. Tap the button and watch what one billionaire does to the average income in the room.
This is the same exercise that’s in the app.
- Average income (mean)
- $56,400
- The middle person (median)
- $53,500
Which one to use
The median, when a few values run far out
Income, home prices, how long people wait on hold. A few extreme values pull the mean away from what a typical person sees, which is why household income and home prices are usually reported as medians.
The mean, when values bunch up evenly
Test scores in one class, the heights of a group of adults, how late the bus usually runs. When there’s no long tail, the two agree, and the mean uses every value.
Both, when it matters
If the mean and median are far apart, that gap is the story. It tells you a few values are pulling hard in one direction.
Where you’ll see it go wrong
“The average home here sold for $900,000” can be true because three mansions sold while most houses went for far less. “Average salary” at a small company can include the founder’s. Whenever someone quotes an average, it’s worth asking which one, and whether a few big numbers are hiding in it.
Questions people ask
Is the average the mean or the median?
Usually the mean. When people say “average” without saying which, they almost always mean add up and divide. Statisticians call the median an average too, which is part of the confusion.
When is the median better than the mean?
When the data is lopsided, with a few values much bigger or smaller than the rest. Incomes and home prices are the classic cases, which is why they’re usually reported as medians.
What about the mode?
The mode is the value that shows up most often. It’s useful for things you can’t really average, like the shoe size a store sells most, and much less useful for money or time.
Learn it by doing it
Module 7, “Averages That Lie,” teaches this in four five-minute lessons, starting with Dre, a cafeteria and a billionaire.
Data to AI is five-minute lessons on how AI works, starting with the data on your phone, for curious teens, parents and grandparents. No math needed. The first lesson runs right here in your browser.