How this statistics calculator works
Descriptive statistics summarise a list of numbers with a few key figures. This calculator parses every valid number you enter — separated by commas, spaces or line breaks — and reports the most common measures of central tendency (mean, median, mode) and spread (range, variance, standard deviation).
The mean is the sum divided by the count. The median is the middle value once the numbers are sorted, or the average of the two middle values when the count is even. The mode is the value that occurs most often; if every value is unique there is no mode, and if several values tie they are all listed. Variance measures the average squared distance from the mean, and the standard deviation is its square root, returning the spread to the original units.
Formulas at a glance
| Statistic | Formula |
|---|---|
| Mean (x̄) | Σx / n |
| Median | middle value of sorted data |
| Range | max − min |
| Variance (population) | Σ(x − x̄)² / n |
| Variance (sample) | Σ(x − x̄)² / (n − 1) |
| Std deviation (population) | √(Σ(x − x̄)² / n) |
| Std deviation (sample) | √(Σ(x − x̄)² / (n − 1)) |
Reference note: sample statistics use n − 1 (Bessel's correction) and are appropriate when your numbers are a sample drawn from a larger population; population statistics use n when your numbers are the entire group.
Frequently asked questions
- How do I calculate the mean?
- Add up all the numbers to get the sum, then divide by how many numbers there are. The result is the mean, also called the average.
- What's the difference between mean, median and mode?
- The mean is the average (sum ÷ count). The median is the middle value of the sorted data (or the average of the two middle values). The mode is the most frequent value — there can be one, several or none.
- How do I calculate standard deviation?
- Find the mean, subtract it from each value and square the result, then average those squared differences to get the variance. The standard deviation is the square root of the variance. Use n − 1 for a sample and n for a population.
- What's the difference between sample and population standard deviation?
- Population standard deviation divides by n and is used when your data is the whole group. Sample standard deviation divides by n − 1, giving a less biased estimate when your data is a sample from a larger population.
- What is the range?
- The range is the largest value minus the smallest value — a quick measure of how spread out the data is.
- Is my data uploaded anywhere?
- No. Every calculation runs locally in your browser. Your numbers are never sent to a server or uploaded anywhere.