The word average covers three different statistics that answer different questions. The mean is the total divided by the count and uses every value. The median is the middle value once sorted and ignores how extreme the outliers are. The mode is simply the value that occurs most often, and is the only one that works on non-numeric categories.
When the three disagree, the data is telling you something. A mean well above the median means a long right tail, which is why average income is always higher than median income: a handful of very large values pull the mean up while leaving the middle where it is. For skewed data the median is almost always the more honest single number to quote.
Below the calculator sits the mean, median and mode for illustrative datasets table: 5 rows — 4, 8, 15, 16, 23, 42, 8 at one end, 2, 2, 3, 9, 9, 40 at the other — which is usually faster than entering a value you have seen before. It loads pre-filled, with your numbers at 4, 8, 15, 16, 23, 42, 8, and the answer updates on every keystroke after that. The 4 bands (low mean at one end, very high mean at the other) exist to answer the question a number on its own cannot: is this high, low or ordinary? Standard Deviation Calculator and Variance Calculator are the nearest neighbours to this one.
The formula
Σx- The sum of all values
n- How many values there are
Median- The middle value, or the mean of the two middle values
Mode- The most frequently occurring value
How to use this calculator
- Paste or type your numbers, separated by commas or spaces.
- The gauge shows the mean.
- Median, mode and range appear below.
- Compare the mean with the median to judge how skewed the data is.
Worked examples
The list 4, 8, 15, 16, 23, 42, 8
The sum is 116 across 7 values, so the mean is 16.5714. Sorted, the middle value is 15, and 8 appears twice so it is the mode. The mean exceeds the median because 42 is pulling it up.
What one outlier does
Remove the 42 and the mean falls to 12.3333 while the median barely moves, to 11.5. That resistance to extreme values is the median main virtue.
Checking the 1, 2, 3, 4, 100 row
The reference table lists 1, 2, 3, 4, 100, giving Mean: 22.000, Median: 3.000, Mode: none, Mean minus median: +19.000. Entering that above should reproduce the same figures — if it does not, the input is being read differently to the way the table assumes.
How to read your score
Frequently asked questions
Which average should I use?
The median for skewed data such as income, house prices or response times. The mean when the data is roughly symmetric and you need it to feed further calculations.
What if no value repeats?
The data has no mode. That is common with continuous measurements, which is why the mode is mostly used on categories and counts rather than measurements.
Can a dataset have more than one mode?
Yes. Two values tying for most frequent makes it bimodal, which often signals two distinct groups mixed together. This page reports the first of any tie.
Why is the mean sensitive to outliers?
Because every value enters the sum at full weight. One value ten times larger than the rest shifts the mean substantially, while the median only cares about position.
What do the bands under the mean mean?
They label the figure so it can be read without a reference point of your own: Low mean up to 10; Moderate mean from 10 to 25; High mean from 25 to 60; Very high mean from 60 upwards. The band is a reading aid only — the number itself is exact, and a value sitting just over a boundary is not meaningfully different from one just under it.
What formula does the Mean Median Mode Calculator use?
It computes Mean = Σx ÷ n; Median = middle value when sorted, where Σx is the sum of all values; n is how many values there are; Median is the middle value, or the mean of the two middle values; Mode is the most frequently occurring value. The same expression is printed on the page above the inputs, so the result can be reproduced by hand or in a spreadsheet.
How the three averages diverge
| Dataset | Mean | Median | Mode | Mean minus median |
|---|---|---|---|---|
| 4, 8, 15, 16, 23, 42, 8 | 16.571 | 15.000 | 8 | +1.571 |
| 5, 5, 5, 5, 5 | 5.000 | 5.000 | 5 | +0.000 |
| 1, 2, 3, 4, 100 | 22.000 | 3.000 | none | +19.000 |
| 10, 20, 30, 40, 50 | 30.000 | 30.000 | none | +0.000 |
| 2, 2, 3, 9, 9, 40 | 10.833 | 6.000 | 9 | +4.833 |
A large positive gap between mean and median indicates a long right tail.