Standard Deviation Calculator
Standard Deviation Calculator
Standard deviation quantifies the amount of variation or dispersion in a dataset. It tells you whether data points tend to be close to the mean or spread across a wide range.
Conversion Formula
σ = √[Σ(xᵢ - μ)² / N]. First find the mean (μ), then compute the squared difference of each value from the mean, average them, and take the square root.
Step-by-Step Examples
10, 12, 23, 23, 16, 23, 21, 16 = σ = 4.8990, σ² = 24.0, μ = 18.0
The values vary moderately around the mean of 18.
5, 5, 5, 5, 5 = σ = 0
All values are identical, so there is no variation.
Frequently Asked Questions
What does standard deviation tell you?
Standard deviation measures how spread out values are from the mean. A low standard deviation means values cluster near the mean; a high one means they are spread out.
What is the difference between population and sample standard deviation?
Population standard deviation divides by N; sample standard deviation divides by N-1 (Bessel's correction). This calculator uses population standard deviation.
What is variance?
Variance is the square of standard deviation. It represents the average squared distance from the mean.
Can standard deviation be negative?
No. Standard deviation is always zero or positive because it is the square root of variance, which is a sum of squared differences.
What is a good standard deviation?
It depends on context. A "good" standard deviation is relative to the mean and the specific application. Compare it using the coefficient of variation (σ/μ).