Standard Deviation Calculator
Calculate standard deviation, variance, and mean for a sample or population data set.
About the Std Deviation Calculator
Standard deviation measures how spread out a set of numbers is from its average — a small standard deviation means values cluster tightly around the mean, while a large one means they're scattered widely. This calculator computes standard deviation, variance, and mean, with support for both sample and population data.
How It Works
The calculator finds the mean of the data set, then computes each value's squared deviation from that mean, and averages those squared deviations to get variance — dividing by n for a full population, or by n-1 for a sample (Bessel's correction, which produces a better estimate of population variance from a subset of data). Standard deviation is the square root of variance.
Variance = Σ(x − mean)² / (n or n−1); Standard Deviation = √Variance.
Example
Scenario: The sample data set 12, 15, 11, 18, 14, 10.
Result: A mean of about 13.33, with a sample standard deviation reflecting how spread out these six values are around that mean.
Assumptions & Limitations
- 'Sample' mode divides by n−1 (Bessel's correction), appropriate when your data is a sample drawn from a larger population.
- 'Population' mode divides by n, appropriate only when your data represents the entire population being studied, not a subset.
- Requires at least two numbers to compute a meaningful standard deviation.