Standard Deviation Calculator (Population & Sample)
This Standard Deviation Calculator computes both sample and population standard deviation with complete step-by-step explanation.
What Is Standard Deviation?
Standard deviation measures how spread out numbers are from the mean.
Mean Formula
Mean = Σx ÷ n
Population Variance
σ² = Σ(x − μ)² ÷ n
Sample Variance
s² = Σ(x − x̄)² ÷ (n − 1)
Standard Deviation
σ = √Variance
When to Use Sample vs Population?
- Use Population formula when data includes entire population.
- Use Sample formula when data is a subset.
Example
For data: 5, 8, 12, 15, 20
Mean = 12
Variance = 34.8
Standard Deviation = 5.9
This calculator provides instant results and step breakdown for students and researchers.