How to use the average calculator
- Paste or type numbers separated by commas, spaces, semicolons or new lines. Decimal points and negative numbers are fine.
- Read the mean at the top, with median, mode, range, sum and standard deviation in the tiles below.
- Check the formula box to see how each value was calculated from your list.
- Use “Copy all” to grab every statistic in one line.
Features
- Mean, median and mode (including several modes or none)
- Range, minimum, maximum, sum and count
- Sample (n − 1) and population (n) standard deviation and variance
- Accepts commas, spaces, semicolons and line breaks; flags anything that isn't a number
- Formulas shown step by step with your numbers
The formulas
For a list of n values x₁ … xₙ:
- Mean (average) = sum of all values ÷ n.
- Median = the middle value after sorting; with an even count, the average of the two middle values.
- Mode = the value(s) that appear most often. If every value appears once there is no mode.
- Range = maximum − minimum.
- Population variance σ² = Σ(x − mean)² ÷ n; population standard deviation σ = √σ².
- Sample variance s² = Σ(x − mean)² ÷ (n − 1); sample standard deviation s = √s².
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9: the sum is 40 and n is 8, so the mean is 5. The sorted middle values are 4 and 5, so the median is 4.5. The mode is 4 (appears three times). The range is 9 − 2 = 7. The squared deviations from the mean add up to 32, so the population variance is 32 ÷ 8 = 4 and σ = 2; the sample variance is 32 ÷ 7 ≈ 4.571 and s ≈ 2.138.
Sample or population?
Use the population figures when your list is the entire group you care about (every student in one class). Use the sample figures when the list is a sample drawn from a larger group and you want to estimate that group's spread; dividing by n − 1 corrects the bias of a small sample. Spreadsheet functions STDEV.S and STDEV.P correspond to the sample and population values here.