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In statistics, explained variation measures the proportion to which a mathematical model accounts for the variation of a given data set. Often, variation is quantified as variance ; then, the more specific term explained variance can be used.
An advantage of variance as a measure of dispersion is that it is more amenable to algebraic manipulation than other measures of dispersion such as the expected absolute deviation; for example, the variance of a sum of uncorrelated random variables is equal to the sum of their variances. A disadvantage of the variance for practical applications ...
A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion.
Thus, this grouping fails to explain the variation in the overall distribution (yellow-orange). An attempt to explain the weight distribution by grouping dogs as pet vs working breed and less athletic vs more athletic would probably be somewhat more successful (fair fit). The heaviest show dogs are likely to be big, strong, working breeds ...
The coefficient of variation fulfills the requirements for a measure of economic inequality. [ 20 ] [ 21 ] [ 22 ] If x (with entries x i ) is a list of the values of an economic indicator (e.g. wealth), with x i being the wealth of agent i , then the following requirements are met:
Standard deviation is a widely used measure of the spread or dispersion of a dataset. It quantifies the average amount of variation or deviation of individual data points from the mean of the dataset. It uses squared deviations, and has desirable properties. Standard deviation is sensitive to extreme values, making it not robust. [7]
Magnetic variation, difference between magnetic north and true north, measured as an angle; p-variation in mathematical analysis, a family of seminorms of functions; Coefficient of variation in probability theory and statistics, a standardized measure of dispersion of a probability distribution or frequency distribution
In mathematics, the total variation identifies several slightly different concepts, related to the (local or global) structure of the codomain of a function or a measure.For a real-valued continuous function f, defined on an interval [a, b] ⊂ R, its total variation on the interval of definition is a measure of the one-dimensional arclength of the curve with parametric equation x ↦ f(x ...