Variance Calculator

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• From Statistics

Understanding Variance

What is Variance?

Variance measures how spread out data is from the mean. It's the average of the squared deviations from the mean. Larger variance means more spread; smaller variance means data is clustered closer to the mean.

Formulas

Sample Variance (s²):

Population Variance (σ²):

Sample vs. Population Variance

• Sample Variance (s²):
  • Uses (n - 1) in denominator (Bessel's correction)
  • Provides unbiased estimate of population variance
  • Use when working with a sample from larger population
• Population Variance (σ²):
  • Uses n in denominator
  • Exact variance of the population
  • Use when you have data for entire population

Variance vs. Standard Deviation

• Variance (s² or σ²):
  • In squared units (e.g., dollars²)
  • Mathematically convenient for calculations
  • Used in ANOVA, regression analysis
• Standard Deviation (s or σ):
  • Square root of variance: σ = √(σ²)
  • In original units (e.g., dollars)
  • More intuitive for interpretation

Coefficient of Variation (CV)

When to Use Variance

• Quality Control: Monitor process consistency
• Finance: Measure investment risk (volatility)
• ANOVA: Compare variance between/within groups
• Regression: Partition variance explained by model
• Hypothesis Testing: F-tests for equality of variances

Properties of Variance

• Always non-negative (≥ 0)
• Variance of constant = 0
• Adding constant doesn't change variance
• Multiplying by constant scales variance by constant²
• Sensitive to outliers (uses squared deviations)