Utilore

Average Calculator

Paste a column from a spreadsheet or type the numbers separated by spaces, commas or new lines. The mean appears at once, with the median, the mode, the smallest and largest, the range and both standard deviations underneath. Nothing is sent anywhere — the numbers stay in this tab.

Paste or type the numbers — separated by spaces, commas or new lines. Everything is worked out as you type.

Mean —

Median
—
Mode
—
Sum
—
Smallest
—
Largest
—
Range
—
Standard deviation, sample
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Standard deviation, population
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Nothing is sent anywhere — the numbers stay in this tab. Two of the results deserve a word. The mode can be missing entirely, when no value repeats, and there can be several of them; showing one number regardless would invent a pattern that is not in the data. And there are two standard deviations: the sample one divides by n−1 and the population one by n. On ten numbers they differ by about five per cent, on three by more than twenty — so pick by whether your numbers are all of the data or a part of it.

Nearby: Percentage Calculator, Grade Calculator, GPA Calculator, Random Number Generator

How to use

  1. Put the numbers in the box. Spaces, commas, semicolons and new lines all work as separators, so a column pasted from a spreadsheet needs no cleaning up.
  2. The mean appears immediately; the rest of the figures are in the list below it.
  3. For a weighted mean, tick the box and enter the weights in the same order as the numbers.
  4. If the count of weights does not match the count of numbers, a note says so — anything left without a weight is not counted.

Good to know

There are two standard deviations, and they are different numbers

The sample standard deviation divides by n−1, the population one by n. Which is correct depends entirely on what your numbers are: all of the data, or a sample drawn from something larger. On ten numbers the two differ by about five per cent; on three, by more than twenty. That is far too much to call rounding, and it is why this page shows both with their names rather than picking one and hoping. If your numbers are every measurement you care about — the marks of everyone in the class — use the population figure. If they are a sample meant to say something about a larger group, use the sample figure.

The mode can be missing, and there can be several

The mode is the value that occurs most often, and it is the only one of these figures that sometimes does not exist. In 1, 2, 3 nothing repeats, so there is no mode at all — and a calculator that answers «1» has invented a pattern the data does not contain. There can also be more than one: in 1, 1, 2, 2, 3 both 1 and 2 are modes. This page says «none» when there is none and lists all of them when there are several.

Mean and median answer different questions

The mean is the total shared out equally; the median is the value in the middle when the numbers are sorted. On tidy data they land close together, and on skewed data they part company: nine people earning 30 and one earning 300 have a mean of 57 and a median of 30. The mean is right if you care about the total — a payroll, a fuel bill. The median is right if you want the typical case, because a single extreme value moves the mean a long way and the median hardly at all.

Frequently asked questions

How should I separate the numbers?

However is convenient: spaces, commas, semicolons, new lines or a mix. A column copied straight out of a spreadsheet works as it is. Negative numbers and decimals with a dot are understood.

Can I use a comma as a decimal point?

Yes, when the numbers are separated by something else — «1,5 2,5» reads as one and a half and two and a half. If commas are the only separators, they are treated as separators: «1,2,3» is three numbers. A lone «1,5» is read as two numbers, so write 1.5 if you mean one and a half.

Which standard deviation should I use?

Population if your numbers are the whole group you are describing; sample if they are a sample from a larger group you want to draw conclusions about. When in doubt in a statistics course, it is usually the sample one — that is what «s» means in most textbooks, and what a spreadsheet's STDEV gives you.

What is a weighted mean for?

For when the numbers do not count equally. Two shops sell at 100 and 200, but you bought nine items at the first and one at the second: the average price across shops is 150, the average price you paid is 110. Tick the weights box and enter 9 and 1.

Are my numbers sent anywhere?

No. Everything is worked out in this tab; nothing is sent to a server, stored or logged. The page works with the network switched off, and closing the tab clears it.

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