Variance

Variance is the expected squared deviation of a random variable from its mean. It measures spread in squared units of the variable.

Expected value: The probability-weighted average value of a random variable. Variance averages squared deviations using the same probability-weighting principle.
Random variable: A function that assigns a numerical value to each outcome in a random experiment. Variance describes the distribution of values assigned by a random variable.
Analysis of variance: A statistical method that compares group means by partitioning observed variability. It uses variance decomposition to test whether group means differ.
Mean absolute deviation: The average absolute distance of observations from a specified center. It measures spread without squaring deviations, so extreme values have less influence.
Standard deviation: The nonnegative square root of variance, expressed in the variable’s original units. Taking its square root converts variance into a directly comparable measure of spread.
Probability distribution: A description of the possible values of a random variable and their probabilities. The distribution supplies the weights used to compute expected squared deviations.
Portfolio variance: The variance of a portfolio’s return, determined by asset weights and return covariances. It quantifies investment risk while showing how asset relationships affect total spread.
Median absolute deviation: The median of absolute deviations from a sample median or another specified center. Its median-based construction is more robust to outliers than variance.
Computational formula for variance: The identity expressing variance as the expected square minus the square of the expectation. This equivalent formula often simplifies calculations from a probability distribution.
Mean: A measure of central location calculated as an arithmetic or probability-weighted average. Variance measures deviations from this central value.

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