desviació

Desviació (Catalan for deviation) is a general term that describes how far a quantity lies from a reference value, such as a target, a norm, or the mean of a dataset. In statistics, desviació refers to measures of dispersion that describe how spread out a set of observations is around a central value. Deviation can be considered at two levels: the deviation of individual observations from a central reference, and aggregate dispersion measures calculated from all deviations in a data set.

For an individual observation xi in a dataset with mean x̄, the deviation is xi − x̄. The absolute deviation is |xi − x̄|, while the squared deviation is (xi − x̄)². The variance is the average of squared deviations: for a population, σ² = (1/N) Σ (xi − x̄)²; for a sample, s² = (1/(n−1)) Σ (xi − x̄)². The standard deviation is the square root of the variance and expresses dispersion in the same units as the data. The mean absolute deviation uses the average of |xi − x̄|.

Other forms exist, such as the mean absolute deviation from a target, and robust measures that reduce sensitivity to outliers. Desviació is thus a fundamental concept in data analysis, facilitating comparisons of variability across datasets, processes, or over time. It underpins risk assessment in finance, quality control in manufacturing, and the assessment of measurement error.

See also: dispersion, variance, standard deviation, mean absolute deviation.