Formula:
Population Variance (σ²) = Σ(xᵢ - μ)² / N
Sample Variance (s²) = Σ(xᵢ - x̄)² / (n - 1)
Theory:
Variance quantifies the spread or dispersion of data points around their mean. A small variance indicates that data points are clustered closely around the mean, while a large variance suggests they are spread out over a wider range.
Population Variance (σ²): This is used when your dataset includes every member of the entire group you are interested in (the population). The sum of squared differences from the mean is divided by N, the total number of population members.
Sample Variance (s²): This is used when your dataset is a smaller subset (a sample) taken from a larger population. To provide an unbiased estimate of the true population variance, the sum of squared differences from the sample mean is divided by n-1 (the sample size minus one), known as Bessel's correction.
Step-by-step Calculation:
