Average Calculator
Type or paste a list of numbers and this calculator instantly works out the mean (the everyday average), median, mode, range, standard deviation and variance, along with the minimum, maximum, count and sum. Separate the numbers with commas, spaces or new lines.
How each figure is calculated
Mean = Sum of all values ÷ Count of values
The median is the middle value once the numbers are sorted, or the average of the two middle values when the count is even. The mode is the value or values that appear most often; if every value appears once, there is no mode. The range is the maximum minus the minimum, a quick measure of how spread out the numbers are.
Standard deviation measures how far the numbers typically sit from the mean. The population version divides by the count and treats your list as the entire group; the sample version divides by one less than the count, which corrects for the extra uncertainty of estimating from a sample. Variance is standard deviation before the square root is taken. Use the sample versions when your numbers are a subset of a larger group you're trying to describe, and the population versions when they are the whole group.
Worked example
For the numbers 4, 8, 6, 5, 3, 8:
| Count | 6 |
|---|---|
| Sum | 34 |
| Mean | 5.666667 |
| Sorted | 3, 4, 5, 6, 8, 8 |
| Median | (5 + 6) ÷ 2 = 5.5 |
| Mode | 8 (appears twice) |
| Range | 8 − 3 = 5 |
Mean vs median: which one to trust
The mean is pulled toward extreme values; the median is not. A neighborhood of nine $300,000 homes and one $3,000,000 mansion has a mean price over $570,000, a number nobody's house is actually near, while the median stays at $300,000. When a data set has outliers, such as salaries, home prices or reaction times, the median usually describes the "typical" value better than the mean.
The mode is most useful for categorical or repeated data, such as the most common shoe size sold or the most frequent score on a quiz. With continuous data where few values repeat exactly, the mode often isn't meaningful, which is why the calculator reports "no repeated value" when every entry is unique.
Frequently asked questions
What is the difference between mean and average?
They are the same thing in everyday use. "Average" most commonly refers to the mean (sum divided by count), though median and mode are also technically types of average. This calculator reports all three so you can see how they differ.
How do I find the median of an even list of numbers?
Sort the numbers, then average the two middle values. For 2, 4, 6, 8 the middle two are 4 and 6, so the median is (4 + 6) ÷ 2 = 5.
What if there is more than one mode?
A list can have more than one most-frequent value; the calculator lists all of them. If every value appears the same number of times, including only once each, there is no single mode and the calculator says so.
Can I paste numbers from a spreadsheet?
Yes. The calculator reads any numbers it finds in the text, so commas, spaces, tabs and line breaks all work as separators. Non-numeric text is ignored.
Should I use population or sample standard deviation?
Use the sample version (dividing by count minus one) when your numbers are a sample drawn from a larger group you're trying to estimate, which is the common case in surveys and experiments. Use the population version when your list is the entire group, with nothing left out.
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Last updated . Formulas are shown on the page and checked against the worked example.
This calculator is for general information and education only. It is not professional advice. Confirm important decisions with a qualified adviser.