The average (arithmetic mean) of a list of numbers is their sum divided by how many there are. For 12, 15, 15, 18, 22, 25 and 31 the sum is 138, the count is 7 and the mean is 19.71. The median is the middle value (18) and the mode is the most frequent value (15).
How do you calculate an average?
In everyday use, โaverageโ means the arithmetic mean: add all the numbers and divide by how many numbers there are. If your five test scores are 6, 7, 7, 8 and 9, the sum is 37 and the mean is 7.4. Statisticians distinguish three measures of centre, each answering a slightly different question, and the calculator gives all of them.
Mean, median and mode
| Measure | How | Best when |
|---|---|---|
| Mean | Sum รท count | Data are roughly symmetric, no extreme outliers |
| Median | Middle value after sorting | Skewed data such as incomes or house prices |
| Mode | Most frequent value | Categories or repeated values, such as shoe sizes |
For an even count, the median is the mean of the two middle values. A set can have no mode (all values different) or several. Salaries show the difference well: if nine people earn โฌ3,000 and one earns โฌ30,000, the mean is โฌ5,700 but the median is โฌ3,000. That is why Dutch statistics bureau CBS often reports median income, not the mean.
Spread: range and standard deviation
The range is the largest minus the smallest value. The standard deviation measures how far values typically are from the mean. The population version divides by n and is used when you have the entire group. The sample version divides by n โ 1 and is used when your numbers are a sample drawn from a larger population. The calculator shows both so you can choose.
Geometric mean
For growth rates and ratios the geometric mean is more appropriate: the n-th root of the product. If an investment grows 10% and then 50%, the geometric mean growth is โ(1.1 ร 1.5) โ 1 = 28.5% per period, not 30%. It requires positive numbers, which is why the tool only shows it for those. For returns on investments see the Investment Return Calculator.
Averages with percentages and grades
To average percentages of different group sizes, use a weighted mean rather than averaging the percentages. For percentage questions use the percentage calculator. Student grades on the Dutch 1 to 10 scale are averaged the same way, with weights if the school uses them.
How to use this calculator
- Type or paste your numbers, separated by commas, spaces or line breaks.
- The tool ignores anything that is not a number.
- Read the mean, median, mode, range, minimum and maximum.
- Compare mean and median to see whether outliers pull the average.
Key figures at a glance
| Mean | Sum รท count |
|---|---|
| Median | Middle value |
| Mode | Most frequent value |
| Sample SD | Divides by n โ 1 |
Frequently asked questions
Add them up and divide by how many numbers there are.
The mean is the arithmetic average and is affected by outliers. The median is the middle value and is more robust.
Yes. If two values occur equally often, the data are bimodal.
An average in which some values count more than others, calculated as ฮฃ(value ร weight) รท ฮฃ weights.
Often the median, because it is less distorted by very high incomes.