Standard Deviation Calculator
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Mean, variance, and standard deviation for a sample or an entire population.
Dataset
Separate values with commas or spaces.
Standard deviation
2.1381
Sample · mean 5 · 8 values
- Variance
- 4.5714
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Standard deviation
Standard deviation measures how spread out a dataset is around its mean. A small standard deviation means values cluster tightly around the average; a large one means they are more spread out. Variance is the standard deviation squared — it is calculated first, then the square root gives the standard deviation in the same units as the original data.
Use sample standard deviation (dividing by n − 1) when your data is a subset used to estimate a larger population — this is the more common case and slightly increases the result to correct for bias. Use population standard deviation (dividing by n) only when your dataset includes every member of the group you care about.
Example: for the dataset 2, 4, 4, 4, 5, 5, 7, 9 (mean = 5), the sample standard deviation is about 2.14, while the population standard deviation is about 2.00 — the sample version is always slightly larger for the same data.
Common questions
Should I use sample or population standard deviation?
Use sample (n − 1) when your numbers are a subset of a larger group you're trying to draw conclusions about — the most common case. Use population (n) only when your dataset is the entire group of interest.
Why is variance shown too?
Variance is the average squared deviation from the mean and is used directly in many statistical formulas. Standard deviation (its square root) is easier to interpret because it uses the original units.