Use the calculator below to find the arithmetic mean of a list of numbers. In addition to the mean, the calculator displays the median, the geometric mean, the highest and the lowest value.
Mean Calculator
Enter your data
Type a list of numbers to calculate the mean. You can separate values with spaces or commas.
How to use the calculator
- Type the numbers separated by spaces or commas in the input field.
Example:
10 20 30or10, 20, 30. - Click Calculate or press Enter to see the results.
- The calculator shows the arithmetic mean, median, geometric mean (when all values are positive), highest value, lowest value and sum.
- See the step-by-step solution below the result to understand how each statistic was obtained.
Formulas
| Statistic | Formula | Example (2, 4, 6) |
|---|---|---|
| Arithmetic mean | x̄ = (x₁ + x₂ + … + xₙ) ÷ n | (2+4+6) ÷ 3 = 4 |
| Median (odd n) | Middle value of sorted data | 2, 4, 6 → 4 |
| Median (even n) | (xn/2 + xn/2+1) ÷ 2 | (4+6) ÷ 2 = 5 (for 2,4,6,8) |
| Geometric mean | GM = ⁿ√(x₁ × x₂ × … × xₙ) | ³√(2×4×6) ≈ 3.634 |
| Maximum | Highest value in the list | 6 |
| Minimum | Lowest value in the list | 2 |
Frequently asked questions about mean
What is arithmetic mean?
The arithmetic mean is the sum of all values in a set divided by the number of values: x̄ = (x₁ + x₂ + … + xₙ) ÷ n. It is the most commonly used measure of central tendency.
Example: The mean of 4, 8 and 12 is (4 + 8 + 12) ÷ 3 = 24 ÷ 3 = 8.
What is the difference between mean and median?
The mean is calculated by summing all values and dividing by the count. The median is the middle value when data are sorted — for an even number of values, it is the average of the two middle values.
The median is less affected by outliers (extreme values). For example, with salaries the median represents reality better than the mean, which can be skewed by very high values.
What is geometric mean and when to use it?
The geometric mean of n positive numbers is the nth root of the product of all values: GM = ⁿ√(x₁ × x₂ × … × xₙ). It is used when values grow multiplicatively, such as interest rates, cumulative percentage changes or biological growth indicators.
Example: An investment grew 10%, 20% and −5% over three years. The average annual growth rate is the geometric mean of 1.10 × 1.20 × 0.95 ≈ 1.0785, i.e. ~7.85% per year.
How to calculate the median of an even list of numbers?
Sort the values in ascending order and calculate the average of the two middle values. Example: 2, 4, 6, 8 → the two middle values are 4 and 6 → median = (4 + 6) ÷ 2 = 5.
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