Why use this calculator
Standard deviation measures how spread out your data is. It's one of the most important statistical concepts, used in research, quality control, finance, and data analysis.
How to use it
Enter up to 5 values. The calculator computes both population and sample standard deviation, along with mean and variance.
The formula
Population σ = √[Σ(xi - μ)² / N]. Sample s = √[Σ(xi - x̄)² / (n-1)]. The difference is dividing by N vs n-1 (Bessel's correction).
Worked examples
Data: 10, 20, 30, 40, 50
Mean = 30, Population SD = 14.14, Sample SD = 15.81
When people use it
- Quality control
- Financial risk assessment
- Scientific research
- Academic statistics
Tips
- Use sample SD when your data is a subset of a larger population
- Use population SD when you have data for the entire population
- A smaller SD means data is more tightly clustered around the mean
Questions people ask
- When do I use population vs sample standard deviation?
- Use population SD when you have data for every member of the group. Use sample SD (with n-1 denominator) when your data is a sample from a larger population, which is the most common case.