Variance

The expected squared deviation of a random variable from its mean — a fundamental measure of dispersion.

Item-writers love to make you pick the divisor: read the stem for “a sample of…” versus the full population, because the wrong choice is the single most common variance error. The other classic pattern hands you a two-asset portfolio variancew₁²σ₁² + w₂²σ₂² + 2·w₁·w₂·Cov(1,2) — and tests whether you square the weights and keep that factor-of-2 covariance term. Since Cov(1,2) = ρ·σ₁·σ₂, the cross-term’s contribution flips sign with the correlation, so lower correlation shrinks total variance (the engine of diversification); note variance itself never goes negative. Watch units, too: variance is in squared units (e.g., %²), so any answer needing comparable, real-world units points to standard deviation.

Don’t conflate variance with correlation. Variance and covariance are unstandardized and unbounded (they run to ±∞), while correlation is covariance scaled to [−1, +1]. And variance measures spread around the mean, not the mean’s level — two datasets with identical means can have wildly different variances. Memory hook: variance squares, deviation roots it back.

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