standard deviation

Standard Deviation

A measure of how spread out values are around the mean — the square root of the variance, in the same units as the original data.

When you'd see it: Alongside the mean in any statistical summary. Also in A/B testing (required to calculate sample sizes), in quality control (3-sigma rules), in model evaluation (standard error), and in finance (volatility of returns is often expressed as standard deviation of returns).

Why it matters: The mean alone doesn't tell you how reliable or consistent the data is. Two processes with the same mean output but different standard deviations are very different — one is predictable, one is noisy. Standard deviation is the formal measure of that noise, and it anchors most inferential statistics.

Common mistakes: Assuming high standard deviation is always bad or low is always good. In investment returns, high standard deviation (volatility) is the cost of high expected returns. In manufacturing, low standard deviation is the goal. Context decides the verdict.

Related mean, variance, normal distribution, outlier, Z-score