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In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation (SD) is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure
Algorithms for calculating variance play a major role in computational statistics.A key difficulty in the design of good algorithms for this problem is that formulas for the variance may involve sums of squares, which can lead to numerical instability as well as to arithmetic overflow when dealing with large values.
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences between groups. It is uses F-test by comparing variance between groups and taking noise , or assumed normal distribution of group, into consideration by ...
The variance of randomly generated points within a unit square can be reduced through a stratification process. In mathematics , more specifically in the theory of Monte Carlo methods , variance reduction is a procedure used to increase the precision of the estimates obtained for a given simulation or computational effort. [ 1 ]
In probability theory, the law of total variance [1] or variance decomposition formula or conditional variance formulas or law of iterated variances also known as Eve's law, [2] states that if and are random variables on the same probability space, and the variance of is finite, then
In statistics, pooled variance (also known as combined variance, composite variance, or overall variance, and written ) is a method for estimating variance of several different populations when the mean of each population may be different, but one may assume that the variance of each population is the same. The numerical estimate resulting from ...
Variance (the square of the standard deviation) – location-invariant but not linear in scale. Variance-to-mean ratio – mostly used for count data when the term coefficient of dispersion is used and when this ratio is dimensionless, as count data are themselves dimensionless, not otherwise. Some measures of dispersion have specialized purposes.
In statistics, the variance function is a smooth function that depicts the variance of a random quantity as a function of its mean.