Math & Statistics · 方差 · Updated 2026-10-25
What Is Variance?
Definition
Variance is the mean of squared deviations — squared units make it awkward to read directly, hence standard deviation. It underpins ANOVA, least-squares regression and portfolio theory.
Formula
σ² = Σ(xᵢ−μ)²/N; portfolio: w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov
Worked Example
For 2/4/6/8: mean 5, squared deviations 9/1/1/9, variance 5, σ≈2.24. Diversification cuts portfolio variance whenever correlation <1.
Common Misconception
"You can compare variance to the mean directly" - different units (squared); take the square root first. "Zero variance means no risk" - it only says historical data was flat, not that the future is safe.
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