Math formula
How to calculate mean
The mean is the arithmetic average of a data set.
Direct answer
Formula
mean = sum of values / number of values
Use the table below to match each symbol with the right input. Keep units consistent before you start.
Mean formula
Start here when you only need the equation and variable names.
Formula
mean = sum of values / number of values
The mean is the arithmetic average of a data set.
Variable meanings
Check each symbol, meaning, and unit before you calculate.
| Symbol | Name | Description | Unit |
|---|---|---|---|
| sum of values | Sum | All data values added together. | Depends on inputs |
| number of values | Count | How many values are in the data set. | Depends on inputs |
When to use this formula
Check that your situation matches the formula before you trust the result.
- Average is a good fit when every value should count equally and outliers are not dominating the data.
Step-by-step method
Follow these steps when you are solving it by hand.
- 1Add every value in the data set.
- 2Count the number of values.
- 3Divide the sum by the count.
Examples
These sample numbers show the order of operations and units.
Four numbers
values
8, 10, 12, 14
- 1.sum = 8 + 10 + 12 + 14 = 44
- 2.count = 4
- 3.mean = 44 / 4 = 11
Result
The mean is 11.
Five numbers
values
3, 5, 5, 7, 10
- 1.sum = 3 + 5 + 5 + 7 + 10 = 30
- 2.count = 5
- 3.mean = 30 / 5 = 6
Result
The mean is 6.
Mistakes to avoid
Small input or unit errors can change the answer a lot.
- Putting the wrong value in the numerator or denominator of the mean formula.
- Skipping signs, order, or sorting rules that change the result.
- Rounding before the last step.
- Assuming a formula applies when the needed input is zero or missing.
Open the Mean, Median & Mode Calculator
Open the calculator for the answer without rewriting the formula.
Enter your values in the related calculator, then compare the output with the hand method above.
Open Mean, Median & Mode CalculatorFAQs
Short answers for common formula questions.
Can I calculate Mean by hand?
Yes. Write the units next to each value, convert rates or measurements first, and round only the final answer.
Why does my Mean result differ from another calculator?
Most differences come from rounding, unit conversions, rate timing, or a slightly different version of the formula.
When is the Mean Median Mode Calculator better than hand math?
Open the Mean Median Mode Calculator to check several scenarios or skip the hand arithmetic.