How to use the Average calculator
- 1Type or paste your numbers, separated by commas, spaces or new lines.
- 2The results update as you type; check that every entry is a plain number, without units or currency symbols.
- 3Compare the mean and median: if they are far apart, a few extreme values are pulling the mean.
- 4Copy the summary to use in a report or spreadsheet.
How it works
The mean adds every value and divides by the count. The median sorts the values and takes the middle one, or the average of the two middle values when the count is even. The mode is the value that appears most often; a list can have several modes or none.
Range is the maximum minus the minimum, a quick measure of spread. The geometric mean multiplies all values together and takes the nth root. It is the right average for growth rates and ratios, and is only defined here for positive numbers.
The mean is sensitive to outliers, while the median isn't. That is why reports on house prices and incomes usually quote the median: a handful of very high values can lift the mean well above what a typical person sees.
Formulas
Mean = (x₁ + x₂ + … + xₙ) ÷ nMiddle value of the sorted list; for even n, the mean of the two middle valuesRange = maximum − minimumGM = (x₁ × x₂ × … × xₙ)^(1/n)All values must be greater than zero.
Worked examples
4, 8, 15, 16, 23, 42
- 1Sum = 108; count = 6; mean = 108 ÷ 6 = 18
- 2Sorted middle values are 15 and 16, so median = 15.5
- 3No value repeats, so there is no mode
- 4Range = 42 − 4 = 38
Mean 18, median 15.5, no mode, range 38.
Quiz scores 3, 7, 7, 2, 9
- 1Sum = 28; mean = 28 ÷ 5 = 5.6
- 2Sorted: 2, 3, 7, 7, 9, so median = 7
- 37 appears twice, so mode = 7
Mean 5.6, median 7, mode 7.
Average growth of +10%, −5% and +20%
- 1Growth factors: 1.10, 0.95, 1.20
- 2Product = 1.254; cube root ≈ 1.0784
- 3The arithmetic mean of the percentages would be (10 − 5 + 20) ÷ 3 ≈ 8.33%
The true average growth is about 7.84% a year, lower than the 8.33% arithmetic mean.
Should I use the mean or the median?
Use the mean when values are fairly symmetric and you want every value to count, such as average test scores in a class. Use the median when data is skewed or contains outliers, such as salaries, response times or property prices. If you're unsure, report both.
What is a weighted average, and can I calculate it here?
A weighted average gives some values more influence than others, like course credits in a GPA. This calculator treats every value equally. To weight values, you can repeat each one according to its weight, or use the GPA or CGPA calculators for grades.
Frequently asked questions
What if there are two modes?
Both are shown. A list where two values tie for the most appearances is called bimodal. If every value appears once, there is no mode.
Can I include negative numbers and decimals?
Yes, for the mean, median, mode, range and sum. The geometric mean needs every value to be positive, so it is not calculated when a list contains zero or negative values.
How do I find the average of percentages?
If each percentage is based on the same size group, a simple mean is fine. For growth rates over time, convert them to factors (5% becomes 1.05) and use the geometric mean.
Why is the mean different from the median?
Extreme values pull the mean toward them, while the median only depends on the middle of the list. A large gap between the two suggests skewed data.
How many numbers can I enter?
Everyday lists work well, from a handful of scores to a column pasted from a spreadsheet. Everything is processed in your browser, not on a server.