Mean, Median and Mode Calculator
The three averages at once — and what it means when they disagree.
All three are called "the average" and they answer different questions.
How the mean, median and mode calculator works
All three are called "the average" and they answer different questions.
The mean adds everything and divides. It uses every value, which is its strength and its weakness: one extreme figure drags it a long way.
The median is the middle value once sorted. It ignores how far away the extremes are, so it barely moves when one appears — which is why incomes and house prices are always reported as medians.
The mode is the most common value, and the only one that works on categories rather than numbers.
When mean and median differ substantially, the data are skewed and the mean alone will mislead. This page shows the gap so you can see it rather than having to check.
Formula: mean = Σx/n; median = middle of the sorted values; mode = most frequent
Worked examples
| Inputs | Mean | Note |
|---|---|---|
| Six values | 18 | mean 18, median 15.5 |
| One extreme value | 22 | mean 22, median 3 — badly skewed |
| With a repeated value | 5 | mode 4 |
FAQFrequently asked questions
What is the difference between mean, median and mode?
Mean is the arithmetic average, median the middle value, mode the most common. They answer different questions and often disagree.
Which average should I use?
The median whenever the data are skewed or contain outliers — which is why incomes and house prices are always reported as medians.
Can there be more than one mode?
Yes. If two values tie for most frequent, both are modes and the data are bimodal.
What if no value repeats?
There is no mode. Reporting one anyway would be meaningless.
What does it mean when the mean is much higher than the median?
A few large values are pulling it up — the distribution has a long right tail, and the mean overstates what is typical.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.