Average Calculator: Mean, Median, Mode and Standard Deviation

Three kinds of average

"Average" usually means the mean, but the median and mode are averages too. They answer slightly different questions, and choosing the right one matters when your data is lopsided.

Mean

Mean = (sum of all values) ÷ (number of values)

For 12, 15, 11, 15, 20, 9, 15, 18 the sum is 115 and there are 8 values, so the mean is 115 ÷ 8 = 14.375.

Median

Sort the values and take the middle one. With an even count, take the mean of the two middle values. Sorted, the example is 9, 11, 12, 15, 15, 15, 18, 20; the middle pair is 15 and 15, so the median is 15.

Mode

The value that appears most often: 15, which appears three times. A list can have several modes, or none at all if no value repeats.

Which average should I use?

Mean uses every value, so it suits data without extreme outliers: test scores, daily temperatures, measurements.
Median ignores how extreme the extremes are, so it suits skewed data such as incomes and house prices. One very large value can pull the mean far above what is typical; the median stays put.
Mode suits categories and repeated values: the most common shoe size, the most frequent rating.

If items should count unequally, such as coursework worth 40% and an exam worth 60%, use the weighted average calculator instead.

Range and standard deviation

The range (largest minus smallest) is the simplest measure of spread. The standard deviation measures how far values typically sit from the mean. The calculator gives two versions:

Population standard deviation (σ) divides by n. Use it when your list is the entire group you care about.
Sample standard deviation (s) divides by n − 1 (Bessel's correction). Use it when your list is a sample and you want to estimate the spread of a larger population. Most statistics courses and spreadsheet functions such as STDEV.S use this version.

For the example list, σ ≈ 3.3889 and s ≈ 3.6228.

Common questions

Can I paste a column from a spreadsheet?

Yes. Values copied from a spreadsheet column arrive on separate lines, which the calculator reads correctly. Remove any header text first.

Why can't I use a comma as the decimal separator?

Because commas separate the values in the list, "1,5" would be read as two numbers, 1 and 5. Write decimals with a period. The other calculators on this site accept either.

How precise are the results?

Calculations use double-precision arithmetic with compensated summation to limit rounding error on long lists, and results are shown to up to 6 decimal places.