Average, Mean, Median & Mode Calculator
Enter a set of numbers and instantly get the mean, median, mode, range, and more. Separate numbers with commas, spaces, or new lines.
What each measure means
| Measure | Definition | Use when |
|---|---|---|
| Mean | Sum divided by count | Values are symmetric, no extreme outliers |
| Median | Middle value when sorted | Outliers present (e.g. income distributions) |
| Mode | Most frequently occurring value | Finding the most common value in a dataset |
| Range | Max minus min | Measuring spread |
| Std deviation | Average distance from the mean | Measuring how spread out values are |
Mean vs median vs mode: when to use which "average"
In everyday speech "average" almost always means the arithmetic mean. In statistics, there are three common "averages" and picking the wrong one gives misleading answers.
The arithmetic mean
Add every value; divide by the count. It uses all the information in the data set, which makes it powerful — but also fragile. A single extreme value (an outlier) drags the mean towards it.
Example: the salaries of five people at a startup are £30k, £32k, £35k, £38k and £900k (the founder). The mean salary is £207k. Nobody at the company is actually paid anywhere near that. Reporting "average salary at this company is £207k" is technically true and completely misleading.
The median
Sort the values; pick the middle one. If there are an even number of values, take the mean of the two middle values. The median is robust — outliers do not move it much.
For the salary example above, the median is £35k. That genuinely reflects what a typical employee earns. This is why house prices, incomes and any skewed distribution are almost always reported as medians, not means.
The mode
The value that occurs most often. Useful for categorical or discrete data (shoe sizes, exam grades, most-frequent shopping-basket items). For continuous measurements like height or income, the mode is usually pointless because no two values are identical.
Beyond the average: range and standard deviation
Two data sets can have identical means and very different characters. Compare:
- Set A: 49, 50, 50, 51 → mean 50, range 2, std dev ≈ 0.7
- Set B: 10, 30, 70, 90 → mean 50, range 80, std dev ≈ 30.5
Both have a mean of 50; only Set A is clustered tightly around it. The standard deviation quantifies how spread out the numbers are: roughly the average distance from the mean.
For a "normal" bell-curve distribution, about 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three (the "68–95–99.7 rule"). Real data is often not normal, so use this as a rule of thumb, not a law.
Population vs sample standard deviation
This calculator returns the sample standard deviation (dividing by n − 1). Use it when your numbers are a sample drawn from a larger population. Divide by n instead if you have the entire population — for a small classroom test that no one else will ever take, for instance. For all practical everyday statistics, the sample version is what you want.
Frequently asked questions
Why is the average I calculated by hand different from this one?
The most common reason: you calculated the mean and are comparing it to the median or vice versa. If both match ours but only for some measures, check for typos — a stray decimal point flips a mean fast.
What separators can I use in the input box?
Commas, spaces, tabs, and newlines all work. You can paste a column from a spreadsheet or a comma-separated list and it will be parsed correctly.
How does the mode work when there is a tie?
If two or more values tie for the highest frequency the calculator reports all of them (the data is bimodal or multimodal). If every value occurs exactly once, there is no mode.
What is the difference between median and mean for household income?
Income distributions are strongly right-skewed — a few very high earners pull the mean up. The UK median household income is around £34k; the mean is closer to £42k. The median gives a better sense of the "typical" household.
Can I use negative numbers?
Yes. The mean, median, standard deviation and range all handle negative values correctly. This matters for temperature series, profit-and-loss figures and any relative measure.