Math & Statistics · 标准差 · Updated 2026-10-25
What Is Standard Deviation?
Definition
Standard deviation (σ) is the square root of variance — the typical spread around the mean. Under normality: ~68% of data within ±1σ, 95% within ±2σ, 99.7% within ±3σ.
Formula
σ = √[Σ(xᵢ−μ)² / N]; sample version divides by (n−1)
Worked Example
Two funds both average 8%, but one has σ≈0.8% and the other σ≈16% — same return, 20x the risk.
Common Misconception
"A big standard deviation is bad" - in investing, volatility is also the source of return; it is a cost only if you cannot bear the drawdown. "Sample std divides by n" - dividing by n-1 is the unbiased estimator; that is the STDEV.S vs STDEV.P difference.
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