TheCalculatory
Math · Everyday Arithmetic Formula verified

Average Calculator

Type or paste a list of numbers, separated by commas, spaces or new lines. Every common average updates as you type.

Numbers

Separate numbers with commas, spaces, or new lines.

Mean (average)
18
6 numbers
Median
15.5
Mode
No mode
Range
38
Std. deviation
12.32

Step-by-step proofCheck by hand

How each statistic is calculated

The mean adds every number in the list and divides by how many numbers there are. The median sorts the list and takes the middle value (or averages the two middle values, for an even-length list). The mode is whichever value repeats most often — a list can have no mode, one mode, or several tied modes. The range is simply the largest value minus the smallest.

The formulas

mean = (sum of values) / n  ·  range = max − min  ·  σ = √(Σ(x − mean)² / n)

Worked example

For 4, 8, 15, 16, 23, 42: the sum is 108, divided by 6 numbers gives a mean of 18. Sorted, the two middle values are 15 and 16, so the median is 15.5. Every number appears exactly once, so there's no mode. The range is 42 − 4 = 38.

Frequently asked questions

What's the difference between mean, median and mode?
The mean adds every number and divides by how many there are — it's what most people mean by "average." The median is the middle value once the numbers are sorted, so it isn't pulled around by one very large or small outlier the way the mean can be. The mode is the value that appears most often; a list can have no mode, one mode, or several tied modes.
How is the median calculated for an even-length list?
Sort the numbers, then average the two values sitting in the middle. For an odd-length list there's a single middle value after sorting, so no averaging is needed.
What does it mean when there's no mode?
It means every number in the list appears exactly once, so nothing repeats more than anything else — there's no single most-common value to report.
Why does this calculator use population standard deviation, not sample?
Population standard deviation divides by the count of numbers you entered (n); sample standard deviation divides by n − 1 instead, which corrects for estimating a larger population from a smaller sample. This calculator treats whatever list you type as the whole population being described, so it uses the plain n version.
Sources and method
  • Standard descriptive statistics (mean, median, mode, range, population standard deviation) — general published mathematics.
Last reviewed: 19 Sep 2026 Sources last verified: 19 Sep 2026 Results use the assumptions explained on this page. Report an error How we check calculations

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