σ Statistics
Standard Deviation Calculator — Population & Sample
Calculate population and sample standard deviation with full step-by-step solution. Enter any set of numbers to get SD, variance, mean, and more.
Frequently Asked Questions
When should I use population vs sample standard deviation? +
Use population SD (σ) when your data is the complete group you're studying. Use sample SD (s) when your data is a subset of a larger population. Sample SD uses N−1 (Bessel's correction) to reduce bias.
What does a standard deviation tell you? +
SD measures how much individual values differ from the mean. A small SD means data points are clustered near the mean. A large SD means data is spread out over a wider range.
What is a normal standard deviation? +
There's no universal 'normal' SD — it depends entirely on your data. In a normal distribution, about 68% of values fall within 1 SD of the mean, 95% within 2 SD, and 99.7% within 3 SD (the 68-95-99.7 rule).