variancën
Variancën, commonly called the variance, is a measure of dispersion in probability and statistics that describes how far a set of values tends to be spread around the mean. For a random variable X with expected value μ, the variance is Var(X) = E[(X − μ)^2]. An equivalent expression is Var(X) = E[X^2] − μ^2 when the expectations exist.
Two common forms are used in practice: the population variance and the sample variance. The population variance
Key properties: Var(X) ≥ 0, with equality only if X is constant almost surely; Var(aX + b) = a^2
Relation to other measures: The standard deviation is the square root of the variance and shares the
Interpretation and uses: Variance quantifies spread; in many fields it informs risk and reliability. In analysis
Computation notes: An equivalent form is s^2 = [Σ Xi^2 − n X̄^2]/(n−1).