Standard Deviation & Variance Calculator

Standard deviation measures the spread or dispersion of a dataset around its mean. Use sample SD (n-1) when working with a subset of a larger population, and population SD (N) when the dataset is the entire population.

To use the Standard Deviation & Variance Calculator, enter your Dataset Values (comma-separated), Calculation Type. The calculator instantly computes Standard Deviation (σ), Variance and more. Results update in real time as you change any input — no submit button needed.

How to Use This Calculator

Enter your Dataset Values (comma-separated) (e.g. 10, 20, 30, 40, 50) and Calculation Type — choose from Sample Std Dev (σ, divides by n-1), Population Std Dev (σ, divides by N). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Mean (μ) = Σx / n

Variance (σ²) = Σ(x - μ)² / (n-1) for sample; ÷ N for population

Standard Deviation (σ) = √Variance

Worked Example

Dataset: 10, 20, 30, 40,

50.

• Mean: ÷ 5 =

30.

• Sum of Squared Deviations: =

1000.

• Sample Variance: 1000 ÷ (5-1) =

250.

• Standard Deviation: √250 = 15.

811.

Understanding Your Result

Statistical results require context: a mean alone is misleading without knowing the standard deviation (spread). Normal distribution reference: 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, 99.7% within ±3 SD. For small sample sizes (n < 30), use t-distributions rather than z-scores. Statistical significance (p < 0.05) does not imply practical significance — effect size (Cohen's d, R², odds ratio) measures real-world importance. Correlation coefficient r: |r| < 0.3 weak, 0.3–0.7 moderate, > 0.7 strong.