varianciáját

In statistics, variance is a measure of how spread out a set of numbers is. In Hungarian, variancia is the term for this concept, and varianciáját is the possessive form used to refer to the variance of a specific variable or dataset (meaning “its variance”).

Mathematically, for a random variable X with expectation μ, Var(X) = E[(X - μ)^2]. This equals the expected value of the squared deviation from the mean. For a finite sample x1, ..., xn, the sample variance is s^2 = (1/(n-1)) Σ (xi - x̄)^2, used to estimate the population variance.

Key properties: variance is nonnegative and equals zero only if X is almost surely constant. If independent variables sum, Var(aX + bY) = a^2 Var(X) + b^2 Var(Y); more generally, for a sum of independent variables, Var(Σ Xi) = Σ Var(Xi).

Interpretation: variance describes dispersion in squared units, and the standard deviation is the square root of the variance, giving dispersion in the original units. Variance is central in many statistical methods, including hypothesis testing, regression, and analysis of variance (ANOVA).

Examples: For a fair six-sided die, Var(X) = 35/12 ≈ 2.9167. For a Bernoulli(p) variable, Var(X) = p(1-p).

In Hungarian scientific writing, one may refer to varianciáját of a statistic to indicate its variance, often in discussions of reliability, precision, or the behavior of estimators.