GUIDE深度 · Deep dive
Variance and Standard Deviation
Variance measures the average squared distance from the mean: compute the mean, subtract it from each value, square, sum, then divide by n (population) or n−1 (sample). Standard deviation is its square root.
Formulas
Population variance = Σ(x−μ)² / n.
Sample variance = Σ(x−x̄)² / (n−1).
Standard deviation = sqrt(variance).
Intuition
Larger variance means more spread.
Standard deviation has the same unit as the data.
FAQ
Why divide by n−1?
n−1 gives an unbiased sample estimate.
Can variance be negative?
No; a sum of squares is non-negative.