Variance Calculator
Calculate both population and sample variance from summary statistics. Also computes standard deviation and standard error of the mean.
Variance measures how spread out values are from the mean.
Population Variance (σ²): σ² = Σ(xᵢ - μ)² / N = (Σx² - (Σx)²/N) / N
Sample Variance (s²): s² = Σ(xᵢ - x̄)² / (n-1) = (Σx² - (Σx)²/n) / (n-1)
Sample variance uses (n-1) instead of n (Bessel's correction) to provide an unbiased estimate of the population variance.
Standard Deviation is the square root of variance, in the same units as the original data.
Standard Error (SE = s/√n) estimates how much the sample mean varies from the true population mean.