Mean, Median and Mode Calculator
Paste numbers in any format and get every summary statistic, plus a note on which average actually fits.
In short
The mean is the total divided by the count, the median is the middle value once sorted, and the mode is the most frequent value. Use the median rather than the mean when the data contains outliers, because a single extreme value drags the mean but barely moves the median.
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Three averages, three different questions
"Average" is ambiguous, and which one you pick changes the answer considerably.
Take these nine salaries: 22, 24, 25, 26, 27, 28, 30, 32 and 180 (thousand).
- Mean: 43.8. Higher than eight of the nine people earn.
- Median: 27. The person in the middle.
- Mode: none, since no value repeats.
The mean is not wrong. It is answering "what would everyone get if the total were shared equally", which is a real question and not the one most people mean when they ask about a typical salary.
This is why official statistics report median income and house prices. One billionaire in the sample moves the mean and leaves the median untouched.
When to use which
| Use | When | Example |
|---|---|---|
| Mean | Data is roughly symmetric with no extreme values | Exam marks, heights, daily temperature |
| Median | Data is skewed or has outliers | Income, house prices, response times |
| Mode | Data is categorical, or you want the most common outcome | Shoe sizes stocked, most frequent rating |
A useful check: if the mean and median differ noticeably, the data is skewed and the median is probably the more honest summary. The tool flags this.
Standard deviation
An average tells you where the middle is and nothing about how spread out the values are. Two datasets can share a mean of 50 while one runs from 49 to 51 and the other from 0 to 100.
Standard deviation measures that spread. For roughly bell-shaped data:
- About 68% of values fall within one standard deviation of the mean
- About 95% within two
- About 99.7% within three
So a mean of 100 with a standard deviation of 15 means roughly two thirds of values sit between 85 and 115. That rule only holds for approximately normal data, which is worth checking before leaning on it.
Sample or population
Population standard deviation divides by n. Use it when your numbers are the entire group you care about, such as the marks of every student in one class.
Sample standard deviation divides by n minus 1. Use it when your numbers are a subset drawn from a larger group you want to describe. The minus one, called Bessel's correction, compensates for the fact that a sample tends to underestimate the true spread.
In practice you almost always want the sample version, which is why it is the headline figure here. The difference shrinks as the dataset grows and is negligible past a few hundred values.
Quartiles and outliers
Quartiles split sorted data into four. The lower quartile is the value a quarter of the way through, the upper quartile three quarters. The gap between them, the interquartile range, holds the middle half of your data and is a spread measure that outliers cannot distort.
The conventional test for an outlier is any value more than 1.5 interquartile ranges beyond a quartile. The tool flags those, but flagging is not the same as removing. Sometimes an outlier is a typing error. Sometimes it is the most important observation in the dataset. Investigate before you delete.
What summary statistics hide
Anscombe's quartet is four datasets with almost identical means, variances and correlations that look completely different when plotted. The Datasaurus Dozen makes the same point more memorably, with one of the datasets forming a picture of a dinosaur.
The lesson holds: summary statistics compress, and compression loses things. If a decision rests on the data, look at the distribution rather than only the numbers describing it.
Frequently asked questions
What is the difference between mean, median and mode?
The mean is the total divided by how many values there are. The median is the middle value once sorted. The mode is the value that occurs most often. They answer different questions, and on skewed data they can be a long way apart.
When should I use the median instead of the mean?
Whenever the data has outliers or is skewed. Incomes, house prices and response times all have a long tail, so a few very large values drag the mean upward while the median stays near the typical value. That is why official statistics almost always report median income rather than mean.
What does standard deviation tell me?
How spread out the values are. A small standard deviation means most values cluster near the mean; a large one means they scatter. For roughly bell-shaped data, about 68% of values fall within one standard deviation of the mean and about 95% within two.
Should I use sample or population standard deviation?
Sample if your numbers are a subset drawn from a larger group you want to describe, which is the usual case. Population if your numbers are the entire group. Sample divides by n minus 1, which corrects a bias that would otherwise underestimate the spread. Both are shown.
How do I enter my numbers?
Any way you like. Commas, spaces, tabs, new lines or a mixture all work, so you can paste a column straight from a spreadsheet without reformatting it.