Variance Calculator
Variance Calculator
Enter your data to calculate variance and related statistics:
- Population or sample variance
- Standard deviation
- Coefficient of variation
- Detailed calculation breakdown
Variance Formulas:
Sample Variance: s² = Σ(x - x̄)² / (n-1)
Population Variance: σ² = Σ(x - μ)² / N
Calculate statistical variance to measure how spread out your data points are from the mean. Essential for data analysis and understanding data variability.
What is Variance?
Variance measures the average squared deviation of data points from the mean. It quantifies how much the data values differ from the average value.
Variance Formulas
Population Variance (σ²)
σ² = Σ(x - μ)² / N
When you have the complete dataset
Sample Variance (s²)
s² = Σ(x - x̄)² / (n-1)
When you have a sample from population
Understanding Variance
| Variance Value | Data Spread | Interpretation | Example |
|---|---|---|---|
| Low Variance | Close to mean | Consistent data | Test scores: 85, 87, 86, 85, 87 |
| Medium Variance | Moderate spread | Some variability | Test scores: 75, 80, 85, 90, 95 |
| High Variance | Wide spread | Highly variable | Test scores: 60, 70, 85, 95, 100 |
Variance vs Standard Deviation
Variance
- Squared units (harder to interpret)
- Always positive
- Sensitive to outliers
- Used in statistical formulas
- Foundation for other statistics
Standard Deviation
- Same units as original data
- Square root of variance
- More intuitive interpretation
- Commonly reported statistic
- Used in normal distribution
Applications of Variance
Finance
- Investment risk assessment
- Portfolio diversification
- Volatility measurement
- Return variability analysis
Quality Control
- Manufacturing consistency
- Process variation monitoring
- Product quality assessment
- Six Sigma applications
Research
- Experimental data analysis
- Hypothesis testing
- ANOVA calculations
- Regression analysis
Variance Calculation Tips
- Check for Outliers: Extreme values greatly increase variance
- Sample vs Population: Use sample variance (n-1) for most real-world data
- Units Matter: Variance is in squared units of original data
- Zero Variance: All data points are identical
- Compare Relatively: Variance is meaningful within context
- Use with Other Statistics: Combine with mean for complete picture
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