Variance in Statistics

Variance

Definition

• Variance is a measure of the spread or dispersion of a set of data from its mean value
• It represents how much the individual data points deviate from the mean

Calculation

• Population variance (σ²): (Σ(xi - μ)²) / N
  • xi: individual data points
  • μ: population mean
  • N: total number of data points
• Sample variance (s²): (Σ(xi - x̄)²) / (n - 1)
  • xi: individual data points
  • x̄: sample mean
  • n: number of data points in the sample

Properties

• Variance is always non-negative (≥ 0)
• A small variance indicates that the data points are close to the mean
• A large variance indicates that the data points are spread out from the mean
• Variance is sensitive to extreme values in the data (outliers)

Interpretation

• Variance is a measure of the average of the squared differences between individual data points and the mean
• A small variance suggests that the data is relatively consistent and predictable
• A large variance suggests that the data is more spread out and less predictable