What is a Average Calculator?
An average is one number standing in for a list, and there are several different ways to compute it — which is why a single figure can be misleading without knowing which one was used. The arithmetic mean is the sum divided by the count. The median is the middle value once the list is sorted. The mode is the value that appears most often. On a skewed list they can disagree sharply: one salary of £1,000,000 in a team of ten pulls the mean far above the median, while the median still describes what a typical person earns.
Standard deviation describes spread rather than centre. It answers how far a typical value sits from the mean, and the two versions differ in one place: the population figure divides by the count, the sample figure divides by the count minus one. The sample version is the right one when your numbers are a sample drawn from something larger — which, in practice, is almost always the case. Divide by n for a complete set, n−1 when generalising.
The tool also computes what the arithmetic mean misses. A weighted mean lets each value count differently, which is how a course grade or an index is calculated. The geometric mean is the correct average for growth rates, ratios and anything multiplied together — using the arithmetic mean on percentage changes overstates the result. The harmonic mean is the correct average for rates such as speeds measured over a fixed distance.
How to calculate an average
- Paste the numbers, separated by commas, spaces or newlines. Thousands separators are not read — write 1500, not 1,500.
- Read the headline: the arithmetic mean of the list.
- Check the median beside it. If the two differ a lot, the list is skewed and the median is usually the fairer description.
- Look at the mode to find anything that repeats, and at the quartiles to see where the middle half of the values sit.
- Add the optional weights — one per number, in the same order — to get a weighted mean. This is what to use for a grade point average or any score where the items are not equally important.
- Compare the geometric and harmonic means when your values are growth rates or speeds rather than plain quantities.
Average Calculator limits and rules
| Item | Limit |
|---|---|
| Mean | Sum divided by count — the arithmetic average |
| Median | Middle value of the sorted list; the average of the two middle values when the count is even |
| Mode | Every value tied for the highest frequency; reported as "no value repeats" when all are unique |
| Quartiles | Linear interpolation between ranks, the common convention for a small sample |
| Sample standard deviation | Divides by n − 1; use when the values are a sample from something larger |
| Population standard deviation | Divides by n; use only when the list is the entire population |
| Weighted mean | Needs exactly one weight per number, in the same order |
| Geometric mean | Multiplicative average; needs every value to be positive |
| Harmonic mean | Reciprocal average of rates; needs every value to be non-zero |
| Input | Separators may be commas, semicolons, spaces, tabs or newlines; decimals and negatives are fine |
| Rejected input | Tokens that are not numbers are listed so you can see what was ignored |
| Not covered | Regression, significance tests, and confidence intervals around the mean |
When to use it
- Working out the mean and median of a set of prices or salaries, where the difference between the two is the whole story.
- Calculating a weighted average grade, where each assessment carries a different proportion of the final mark.
- Finding the spread of a set of measurements with the sample standard deviation, and checking whether one reading is an outlier against the quartiles.
- Averaging growth rates across several years, where the geometric mean is the correct figure and the arithmetic mean overstates every time.
- Finding the mode of a list of response values from a survey, to see which answer was most common.
Is it private?
Everything runs inside your browser. Your text and files are never uploaded, never stored and never seen by anyone else — including me. You can use the tool with the network tab open and watch no request leave the page. Closing the tab erases the input.
Frequently asked questions
The sample version, dividing by n − 1, unless your list is genuinely the entire population and not a sample of something larger. Samples underestimate the spread of the wider group, and the n − 1 correction is there to compensate. If you surveyed a group to say something about a wider one, use the sample figure.
Because the list is skewed. The mean is pulled by every value, so a single very large or very small one moves it; the median only cares about position in the sorted order. For anything following a long tail — incomes, house prices, page views — the median is the better description of a typical value.
When the values are multiplied rather than added: growth rates, ratios, index levels, anything expressed as a factor. Averaging 10%, 20% and 30% returns arithmetically gives 20%, but the true compound return is about 19.3%. The arithmetic mean is always an overestimate for growth.
As the average of the two middle ones. With ten values, the median sits between the fifth and sixth. That is why the median of an even-sized list of whole numbers can be a half-integer.
Yes. If two or more values tie for the highest frequency, the list is bimodal or multimodal and every tied value is reported. A list where nothing repeats has no mode at all, which is different from having one that appears once.
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Written and maintained by Md. Nur Hossain Repon.