Variance Calculator
Calculate variance, standard deviation, and mean with precision. Ideal for researchers, students, and analysts. Instant results with visual data representation.
Understanding the Tool
A responsive web application that computes:
- Arithmetic Mean (Data average)
- Sample Variance (Data spread measurement)
- Population Variance (Complete dataset variation)
- Standard Deviation (Volatility indicator)
Core Formulas (Sample Data)
| Calculation | Formula |
|---|---|
| Mean | μ = (Σx)/n |
| Sample Variance | s² = Σ(x-μ)²/(n-1) |
| Population Variance | σ² = Σ(x-μ)²/n |
| Standard Deviation | σ = √σ² |
How to Use: 3-Step Process
Input
- Enter comma/space-separated values
- Example:
5, 7.2, 15, -3, 0
Calculation
- Automatic real-time computation
- Dynamic chart visualization
Interpretation
- Color-coded statistical outputs
- Exportable results
Frequently Asked Questions
Q: Sample vs Population variance?
A: Use sample variance (n-1) for experimental data; population variance (n) for complete datasets
Q: Why negative variance?
A: Impossible - variance is always ≥0 (sum of squared values)
Q: Minimum data points?
A: 2+ recommended (1 point yields zero variance)
Terminology Glossary
| Term | Definition |
|---|---|
| Degrees of Freedom | n-1 adjustment for sample bias |
| Sum of Squares | Squared deviations total (SS) |
| Bessel’s Correction | n-1 adjustment factor |
| Dispersion | Data spread measurement |
Professional Use Cases
- Academic Research: Validate hypothesis testing
- Financial Analysis: Measure investment volatility
- Quality Assurance: Monitor production consistency
- Machine Learning: Feature scaling reference