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In probability theory and statistics, the index of dispersion, [1] dispersion index, coefficient of dispersion, relative variance, or variance-to-mean ratio (VMR), like the coefficient of variation, is a normalized measure of the dispersion of a probability distribution: it is a measure used to quantify whether a set of observed occurrences are clustered or dispersed compared to a standard ...
This follows from the fact that the variance and mean are independent of the ordering of x. Scale invariance: c v (x) = c v (αx) where α is a real number. [22] Population independence – If {x,x} is the list x appended to itself, then c v ({x,x}) = c v (x). This follows from the fact that the variance and mean both obey this principle.
The red population has mean 100 and variance 100 (SD=10) while the blue population has mean 100 and variance 2500 (SD=50) where SD stands for Standard Deviation. In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable.
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.
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.
Several are standard statistics that are used elsewhere - range, standard deviation, variance, mean deviation, coefficient of variation, median absolute deviation, interquartile range and quartile deviation. In addition to these several statistics have been developed with nominal data in mind.
In estimating the mean of uncorrelated, identically distributed variables we can take advantage of the fact that the variance of the sum is the sum of the variances.In this case efficiency can be defined as the square of the coefficient of variation, i.e., [13]
A key step in the derivation of the binary power law by Hughes and Madden was the observation made by Patil and Stiteler [61] that the variance-to-mean ratio used for assessing over-dispersion of unbounded counts in a single sample is actually the ratio of two variances: the observed variance and the theoretical variance for a random ...