About the Statistics Calculator
A statistics calculator computes the descriptive measures that summarise a dataset: mean, median, range, variance, and standard deviation. Together they describe where the data centres and how widely it spreads, which is the necessary first step before any deeper analysis.
The formula
σ = √( Σ(xᵢ − μ)² / n )μ is the mean, xᵢ each data point, n the count. Variance is the mean squared deviation; standard deviation is its square root, restoring the original units.
How to use this calculator
- 1Enter your Value 1. The field starts at
4, which you can overwrite. - 2Enter your Value 2. The field starts at
7, which you can overwrite. - 3Enter your Value 3. The field starts at
13, which you can overwrite. - 4Enter your Value 4. The field starts at
2, which you can overwrite. - 5Enter your Value 5. The field starts at
9, which you can overwrite. - 6Enter your Value 6. The field starts at
5, which you can overwrite. - 7Read the result straight away — it recalculates as you type, so there is no button to press. Use Share to copy a link that reopens the page with your exact numbers filled in.
Worked example
| Input | Value |
|---|---|
| Value 1 | 4 |
| Value 2 | 7 |
| Value 3 | 13 |
| Value 4 | 2 |
| Value 5 | 9 |
| Value 6 | 5 |
Result
Mean: 6.6667
Std Dev: 3.5901
Variance: 12.8889
Range: 11
Min: 2 Max: 13
Those are the values the page loads with, so you can reproduce this result yourself and then change one field at a time to see what drives the outcome.
Understanding your result
Centre and spread answer different questions and you need both. Two datasets can share a mean of 50 while one ranges from 49 to 51 and the other from 0 to 100. Reporting only the mean would present them as identical, which is why standard deviation belongs alongside it in any summary.
Standard deviation is expressed in the same units as the data, which is why it is preferred to variance for reporting. In roughly normal data, about 68 percent of values fall within one standard deviation of the mean, 95 percent within two, and 99.7 percent within three — the rule that makes standard deviation interpretable rather than merely computable.
Things worth knowing
- Use the sample standard deviation, dividing by n − 1, when your data is a sample from a larger population.
- The mean and standard deviation are both sensitive to outliers. For skewed data, report the median and interquartile range.
- The coefficient of variation — standard deviation over mean — compares spread between datasets with different units.
- A standard deviation of zero means every value is identical.
- Always plot your data. Summary statistics can be identical for datasets that look nothing alike.
Frequently asked questions
What does standard deviation tell me?+
How far values typically sit from the mean. A small standard deviation means the data clusters tightly; a large one means it spreads widely. It is expressed in the same units as the original data.
What is the difference between variance and standard deviation?+
Variance is the average squared deviation from the mean; standard deviation is its square root. Standard deviation is usually reported because squaring puts variance in unintuitive units.
Should I use population or sample standard deviation?+
Use the population version when you have every member of the group. Use the sample version, dividing by n − 1, when generalising from a sample — it corrects a bias that would otherwise understate the spread.
Why report the median as well as the mean?+
Because the mean is pulled by outliers while the median is not. When they differ substantially, the data is skewed, and that gap is itself informative.