About the Average Calculator
This average calculator finds the arithmetic mean of a list of numbers, together with the other measures of central tendency (median and mode) and of spread (range, variance and standard deviation). Paste test scores, sales figures or measurements separated by commas, spaces or line breaks — a column copied from Excel or Google Sheets works too.
When values count differently, such as courses with different credit hours, switch to the Weighted average tab and enter a weight for each value.
How to use
- In the Mean & std. deviation tab, type or paste your numbers separated by commas, spaces or line breaks.
- The mean is shown in large type, followed by the count, sum, median, mode, minimum and maximum.
- Variance and standard deviation are shown both for a population (÷ n) and for a sample (÷ n − 1).
- For a weighted average, open the Weighted average tab and enter a value and a weight (credits, percentage, quantity…) on each row.
Mean vs. median vs. mode
| Measure | How to find it | 1, 2, 3, 4, 100 |
|---|---|---|
| Mean | Sum ÷ count | 22 |
| Median | The middle value when sorted (with an even count, the average of the two middle values) | 3 |
| Mode | The value that occurs most often | None |
As the example shows, one extreme value such as 100 pulls the mean a long way, while the median barely moves. That is why income and house-price statistics usually report the median.
Variance and standard deviation formulas
Square the difference between each value and the mean, then add them up to get the sum of squares.
- Population variance = sum of squares ÷ n; population standard deviation = √variance (Excel VAR.P, STDEV.P)
- Sample variance = sum of squares ÷ (n − 1); sample standard deviation = √variance (Excel VAR.S, STDEV.S)
Example: for 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5 and the sum of squares is 32, so the population variance is 4, the population standard deviation is 2 and the sample variance is 32 ÷ 7 ≈ 4.571429.
How to calculate a weighted average
Weighted average = Σ(value × weight) ÷ Σweights. For example, a grade of 90 in a 3-credit course, 80 in a 2-credit course and 70 in a 1-credit course gives (90×3 + 80×2 + 70×1) ÷ (3+2+1) = 500 ÷ 6 ≈ 83.33. Courses with more credits count more than in the simple mean of 80. The same method works for a GPA: use grade points (4.0, 3.7…) as values and credit hours as weights.
FAQ
How do I enter numbers with thousands separators like 1,000?
Commas are treated as separators between numbers, so type 1000 without the comma. When copying from Excel, set the cell format to General so the numbers are copied without separators.
Should I use the sample or the population standard deviation?
Use the population formula if your data covers the whole group you care about (e.g. every student in a class). Use the sample formula when your data is a sample used to estimate a larger group — the usual case in statistics assignments and research.
Can there be more than one mode?
Yes. If several values share the highest count, all of them are shown. If every value appears only once, the mode is shown as “None”.
What happens to text mixed in with the numbers?
Anything that can’t be read as a number is left out of the calculation, and a note below the input box lists what was ignored.