Find sample and population standard deviation, variance, mean, range, and count from a list of numbers with this free standard deviation calculator.
Mean:
Sum of values ÷ number of values
Population variance:
Σ(x − μ)² ÷ n
Sample variance:
Σ(x − x̄)² ÷ (n − 1)
Standard deviation:
√variance
Standard deviation measures how far values typically spread out from the mean. It helps show consistency, variability, and risk in a dataset.
It is commonly used in statistics, finance, business, science, and quality control.
Your result shows how tightly grouped or spread out the data is around the mean. A smaller standard deviation means the values stay closer to the average.
A larger standard deviation means the values are more widely spread, which can signal more variability or less consistency.
Standard deviation is a measure of how spread out numbers are from their mean.
Variance is the average squared distance from the mean, while standard deviation is the square root of variance.
Use sample standard deviation when the data is a sample from a larger population.
Yes. This calculator works with whole numbers, decimals, and negative values.