In mathematics, univariate refers to an expression, equation, function or polynomial of only one variable. Objects of any of these types involving more than one variable may be called multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials.
The term is commonly used in statistics to distinguish a distribution of one variable from a distribution of several variables, although it can be applied in other ways as well. For example, univariate data are composed of a single scalar component. In time series analysis, the term is applied with a whole time series as the object referred to: thus a univariate time series refers to the set of values over time of a single quantity. Correspondingly, a "multivariate time series" refers to the changing values over time of several quantities. Thus there is a minor conflict of terminology since the values within a univariate time series may be treated using certain types of multivariate statistical analyses and may be represented using multivariate distributions.
In addition to the question of scaling, a criterion (variable) in univariate statistics can be described by two important measures (also key figures or parameters): Location & Variation.
- Measures of Location Scales (e.g. mode, median, arithmetic mean) describe in which area the data is arranged centrally.
- Measures of Variation (e.g. span, interquartile distance, standard deviation) describe how similar or different the data are scattered.
- Grünwald, Robert. "Univariate Statistik in SPSS". novustat.com (in German). Retrieved 29 October 2019.
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