CompleteToolkit

Average Calculator

Mean, median, mode, range and standard deviation from any list of numbers — instantly.

Separate values with commas, spaces or new lines. Non-numeric entries are ignored.

Mean (average)

10

Sum 80 ÷ 8 values

Median

8

middle value

Mode

7

appears 3×

Range

17

3 to 20

Count

8

Minimum

3

Maximum

20

Spread

Standard deviation (sample)

5.424811

n − 1 divisor

Standard deviation (population)

5.074446

n divisor

Variance (sample)

29.428571

Variance (population)

25.75

Sorted values

3, 7, 7, 7, 9, 12, 15, 20

Use the sample standard deviation when your numbers are a sample drawn from a larger group (the usual case in statistics coursework and research). Use population when your list is the entire group you care about.

About this tool

"Average" usually means the mean — add everything up and divide by how many there are — but statistics has three different averages, and they answer different questions. This calculator gives you all of them at once, along with the measures of spread that tell you how tightly your numbers cluster.

The **mean** is the arithmetic average, the familiar one, and it's sensitive to outliers: one enormous value drags it upward. The **median** is the middle value when everything is sorted, which is why income and house-price statistics use it — it isn't distorted by extremes. The **mode** is whatever appears most often, the only average that works for non-numeric categories and the right one when you want "the most common". Seeing all three side by side often reveals more about a dataset than any one alone.

Beyond averages, the calculator reports the range (highest minus lowest), variance, and both forms of standard deviation — sample (n−1 divisor) and population (n divisor) — because coursework and research usually need the sample version while the population version applies when your list is the complete group. Paste numbers separated by commas, spaces or new lines in any mix; non-numeric entries are simply ignored. Everything computes live in your browser.

How to use the Average Calculator

  1. 1Paste or type your numbers — commas, spaces or new lines all work.
  2. 2Read the mean (average) as the headline figure.
  3. 3Compare mean, median and mode — big differences reveal outliers or skew.
  4. 4Use sample standard deviation for coursework and research; population when your list is the whole group.

Frequently asked questions

What's the difference between mean, median and mode?

Mean is the sum divided by the count (the usual 'average'). Median is the middle value when sorted. Mode is the most frequent value. For 1, 2, 2, 100: mean is 26.25, median is 2, mode is 2 — the mean is pulled up by the outlier, which is exactly why the other two exist.

Should I use sample or population standard deviation?

Sample (dividing by n−1) when your numbers are a sample drawn from a larger group — the standard choice in coursework, research and most real analysis. Population (dividing by n) when your list is the entire group you care about. Sample is slightly larger, correcting for the fact that a sample underestimates true spread.

What does standard deviation actually tell me?

How spread out the values are around the mean. A small standard deviation means the numbers cluster tightly; a large one means they're scattered. Two datasets can share an identical mean but look completely different — standard deviation is what distinguishes them.

What if my numbers have no repeats?

Then there's no mode — the tool reports 'None' rather than inventing one, since a mode only exists when at least one value repeats. Mean, median and the spread measures are still calculated normally.