Arithmetic Mean Calculator

What the arithmetic mean calculator does

The arithmetic mean is the plain average, the one almost everyone means by the word. You add all your numbers together and divide by how many there are. This calculator does that, and shows you the sum and the count it used, so you can see the working, not just the answer.

It is the everyday measure of a typical value: the average score, the average price, the average temperature. Below is how it gets there, and the one thing the mean quietly does not tell you.

How to use it

1. Enter your numbers in the box, separated by spaces or commas.
2. Press Calculate to see the count, the sum, and the arithmetic mean, or Reset to clear it.

How the mean is worked out

There is nothing hidden here. The mean is just two steps:

Mean = sum of all the values ÷ how many values there are

So for five numbers, you add the five together and divide by five. The calculator shows you that sum and that count next to the answer, which is a handy check that none of your numbers were dropped or counted twice.

What the mean tells you, and what it hides

The mean uses every single value, which is its strength and its weakness in one. Its strength is that it reflects all your data, so any change to any number moves it. Its weakness is the flip side: one unusually large or small value pulls the mean toward itself, and the rest of the numbers cannot pull it back.

That is why the mean works best when your data is fairly even, with no extreme outliers. When a few values are wildly bigger or smaller than the rest, like a handful of huge salaries in a list of ordinary ones, the mean stops describing a typical value, and the median often tells the truer story. There is a median calculator for exactly those cases.

A worked example, and an outlier

Take the five numbers 2, 5, 7, 9, 12. They add up to 35, so the mean is 35 ÷ 5 = 7. That sits comfortably in the middle of the data, a fair description of a typical value.

Now swap the 12 for 112. The numbers add up to 135, and the mean jumps to 27, even though only one value changed. None of the other four numbers are anywhere near 27. That is the mean's tell: every value pulls on it, so a single outlier can drag it well away from the crowd.

Entering your data, and the rounding

You can separate your numbers with spaces or commas, and the order does not matter, since the mean depends only on the values and how many there are. The calculator reads the numbers out of whatever you type, so a stray space will not trip it.

The sum and the mean are shown at full precision, so a result that does not divide evenly, like 10 divided by 3, will show a long string of decimals. You can round it to whatever suits your work.

Questions people ask

What is the arithmetic mean?

The sum of all your values divided by how many there are. It is the standard average, a single number meant to stand for a typical value in the set.

Is the mean the same as the average?

In everyday use, yes. When people say average they almost always mean the arithmetic mean. In statistics, average is a looser word that can also refer to the median or the mode.

Does one extreme value really change the mean that much?

It can. Because the mean uses every value, a single number far from the rest pulls it noticeably. With strong outliers, the median is usually a better measure of the typical value.

Should I use the mean or the median?

Use the mean when your data is fairly even. Switch to the median when a few values are much larger or smaller than the rest, or when the data is skewed.

References

A quick note on where the methods here come from. The definition of the mean and how it sits among the other measures of central tendency are set out in the NIST/SEMATECH e-Handbook of Statistical Methods, the US government's public statistics reference. OpenStax Introductory Statistics is a free, widely used textbook that covers the mean and its sensitivity to outliers.

1. NIST/SEMATECH e-Handbook of Statistical Methods (measures of location). https://www.itl.nist.gov/div898/handbook/
2. OpenStax, Introductory Statistics (measures of the center of the data). https://openstax.org/details/books/introductory-statistics-2e