Variance
A measure of the spread of values, calculated as the average squared deviation from the mean.
Also known as: Statistical variance, Spread, Dispersion
Category: Concepts
Tags: statistics, measurement, risks, uncertainties, analysis
Explanation
Variance measures how spread out data points are from their mean - specifically, the average of squared deviations from the mean. Higher variance means more spread; lower variance means values cluster tightly. Variance is the square of standard deviation. Why squared: it makes all deviations positive (negatives don't cancel positives), and it penalizes large deviations more heavily. Practical interpretations: low variance means predictability and consistency; high variance means uncertainty and volatility. Applications include: portfolio risk (variance of returns), quality control (variance in production), and uncertainty quantification. Related concepts: standard deviation (square root of variance, same units as data), coefficient of variation (variance relative to mean), and covariance (how two variables vary together). Bias-variance tradeoff: in machine learning, reducing variance (making predictions more consistent) often increases bias (systematic error), and vice versa. For knowledge workers, understanding variance helps: quantify uncertainty and risk, recognize when outcomes are predictable vs volatile, compare variability across different scales, and make better decisions under uncertainty.
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