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Math & Statisticsstatistics

Average / Mean Calculator

Mean, median and mode together with the spread, because which average is right depends on the shape of the data. One extreme value moves the mean and leaves the median where it was.

Also called: mean calculator, average of numbers.

Separate with commas, spaces or new lines.

Mean
13.8333

The mean is 13.83 across 6 values summing to 83. The median is 13.5 and the mode is no repeated value. The mean sits above the median, which means a long right tail is pulling it up. No values fall outside the 1.5 IQR fences, so the mean and median should agree closely.

Mean
13.83
Median
13.5
Mode
no repeated value
How many values
6
Sum
83
Smallest
7
Largest
22
Range
15
First quartile
9.75
Third quartile
17.25
Interquartile range
7.5
Sample standard deviation
5.64
Population standard deviation
5.15
On outliers
No values fall outside the 1.5 IQR fences, so the mean and median should agree closely.
On the shape
The mean sits above the median, which means a long right tail is pulling it up.
How this is calculated
Method and background

How this is calculated

The mean is the sum over the count. It is the right average for roughly symmetric data and the wrong one when a few extreme values pull it: a single very large number moves the mean and leaves the median untouched, which is why incomes are reported as medians. Showing all three averages and the spread alongside lets you see which applies rather than assuming. The gap between the mean and the median is the quickest read on whether the distribution is skewed.

the mean is one of three averages, and which one is right depends on the shape of the data
n
How many values

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

six values

Numbers
12, 18, 7, 22, 15, 9

Mean13.8333

83 over 6; the median is between 12 and 15

Open this example

one extreme value moves the mean and not the median

Numbers
12, 18, 7, 22, 15, 900

Mean162.3333

boundary: the case that decides which average to use

Open this example

Method and limits

What it assumes

  • Numeric values, with anything unparseable ignored.

What it deliberately does not model

  • Quartiles use linear interpolation, which is the spreadsheet convention; other definitions differ slightly on small samples.
  • A summary hides the distribution: two very different datasets can share every statistic here.

Formula version 1.0.0 · definition 1.0.0 · India · Report a problem with this calculator

Frequently asked questions

Should I use the mean or the median?
The median when the data has outliers or a long tail, since one extreme value moves the mean and not the median. The mean when the distribution is roughly symmetric.
Which standard deviation do I want?
Sample, almost always. The n-1 divisor corrects for the mean being estimated from the same data. Use the population divisor only when your data genuinely is every member of the group.