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In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. [1] Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered.
Calculus of variations is concerned with variations of functionals, which are small changes in the functional's value due to small changes in the function that is its argument. The first variation [l] is defined as the linear part of the change in the functional, and the second variation [m] is defined as the quadratic part. [22]
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.
Download as PDF; Printable version; ... A similar formula is applied in analysis of variance, ... and is known as the biased sample variation. Population variance
Since the ratio (n + 1)/n approaches 1 as n goes to infinity, the asymptotic properties of the two definitions that are given above are the same. By the strong law of large numbers , the estimator F ^ n ( t ) {\displaystyle \scriptstyle {\widehat {F}}_{n}(t)} converges to F ( t ) as n → ∞ almost surely , for every value of t : [ 2 ]
The data set [90, 100, 110] has more variability. Its standard deviation is 10 and its average is 100, giving the coefficient of variation as 10 / 100 = 0.1; The data set [1, 5, 6, 8, 10, 40, 65, 88] has still more variability. Its standard deviation is 32.9 and its average is 27.9, giving a coefficient of variation of 32.9 / 27.9 = 1.18
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 ...
In mathematics, variational analysis is the combination and extension of methods from convex optimization and the classical calculus of variations to a more general theory. [1] This includes the more general problems of optimization theory , including topics in set-valued analysis , e.g. generalized derivatives .