Standard Deviation

Definition

A measure of how spread out a dataset is around its mean, expressed in the same units as the data. For a normal distribution, about 68% of values fall within one standard deviation of the mean, 95% within two, and 99.7% within three, the so-called 68-95-99.7 rule. Formula: σ = √(Σ(x − μ)² ÷ N) for a population, or divide by (n − 1) for a sample. Standard deviation underpies risk measurement in finance (volatility), quality control in manufacturing (Six Sigma), and confidence intervals in research.