Is the average the same as the mean?

Yes. In everyday use “average” means the arithmetic mean: add every value together, then divide by how many values there are. The median (middle value) and mode (most common value) are different kinds of average that suit skewed data better.

How do I work out the average by hand?

Add the numbers one by one to get a running total, then divide that sum by the count of values. For 12, 8, 15, 16 and 23: the sum is 74 and there are 5 values, so the average is 74 ÷ 5 = 14.8.

Why does the calculator also show the median and mode?

The mean is pulled toward outliers. If one value is much larger than the rest, the median usually describes the “typical” value better — so we show all three side by side, with the working for each.

Can I average negative numbers or decimals?

Yes. The formula is identical for negatives, decimals and mixed values — the sum can be negative, and so can the mean.

Arithmetic & Factors

Shows the working

Average Calculator

Type in any list of numbers and get the mean instantly — with every step of the working shown, plus the median, mode and range so you can see the whole picture of your data.

Your numbers

5 numbers recognised

Separate with commas or spaces — up to 60 values.

Worked solution

Average (mean)

14.8

5 values totalling 74, shared out equally

Add the values, divide by how many there are: 74 ÷ 5 = 14.8.

Rounded where needed — the mean is exact for the numbers you entered.

The working

4 steps

Write out the data
5 values entered. The mean uses every one of them — nothing is dropped.
12 + 8 + 15 + 16 + 23
Add everything up
The running total after each value is shown in the second column.
Value Running total
12 12
8 20
15 35
16 51
23 74
Sum = 74
Divide the sum by the count
The mean is the value every entry would have if the total were shared out equally.
mean = 74 ÷ 5 = 14.8
sum ÷ how many values
Check the spread of the data
The mean alone can hide outliers — the median and mode show where the data really sits.
Smallest
8
Largest
23
Range
15
Median (middle value)
15
Mode (most frequent)
none

Value	Running total
12	12
8	20
15	35
16	51
23	74

Works instantly in your browser — nothing is uploaded, and the URL keeps your numbers so you can share the exact worked example.

What the average really measures

The mean answers one question: if every value contributed equally, what would each one be? Take five friends who spent £12, £8, £15, £16 and £23 on a night out. The total is £74, and split five ways that is £14.80 each — the average.

Because the mean uses every value, a single extreme number drags it along. That is why this page also works out the median and mode: when the mean and median disagree by a lot, the data is skewed and the median is usually the safer summary.

Average vs median vs mode

The mean is the equal-share value. The median is the middle value once the data is sorted — half the data sits above it, half below. The mode is simply the value that appears most often.

For 12, 8, 15, 16, 23, 42 the mean is 19.5 but the median is 15.5 — the 42 pulls the mean upward. Salaries, house prices and almost anything money-shaped behaves this way, which is why “average salary” headlines are usually the mean while analysts prefer the median.