Variance & Spread
Average squared distance from the mean.
Concept
Why square the deviations
Deviations from the mean always sum to zero, so we square them before averaging. That gives variance; its square root is the standard deviation, back in the original units.
Bigger variance means the data spreads further from center — same average, very different story.
σ² = ∑(xᵢ − x̄)² / n