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This definition encompasses random variables that are generated by processes ... and is known as the biased sample variation. Population variance ... Mathematics portal
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]
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
Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well.
In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those functions.
In statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean.The variance function is a measure of heteroscedasticity and plays a large role in many settings of statistical modelling.
In mathematics, a variable (from Latin variabilis, "changeable") is a symbol, typically a letter, that refers to an unspecified mathematical object. [1] [2] [3] One says colloquially that the variable represents or denotes the object, and that any valid candidate for the object is the value of the variable. The values a variable can take are ...