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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:
While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by ( Freeman 1965 ). Just as with the range or standard deviation , the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller ...
These include Gini's index of mutability, [13] Simpson's measure of diversity, [14] Bachi's index of linguistic homogeneity, [15] Mueller and Schuessler's index of qualitative variation, [16] Gibbs and Martin's index of industry diversification, [17] Lieberson's index. [18] and Blau's index in sociology, psychology and management studies. [19]
Toggle the table of contents. ... Variance is a measure of dispersion, ... and is known as the biased sample variation. Population variance
a measure of the shape of the distribution like skewness or kurtosis if more than one variable is measured, a measure of statistical dependence such as a correlation coefficient A common collection of order statistics used as summary statistics are the five-number summary , sometimes extended to a seven-number summary , and the associated box ...
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 ...
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.
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]