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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.
A frequency distribution is constructed. The centroid of the distribution gives its mean. A square with sides equal to the difference of each value from the mean is formed for each value. Arranging the squares into a rectangle with one side equal to the number of values, n, results in the other side being the distribution's variance, σ 2.
Cumulative probability of a normal distribution with expected value 0 and standard deviation 1. In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its mean. [1]
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
A discrete probability distribution is applicable to the scenarios where the set of possible outcomes is discrete (e.g. a coin toss, a roll of a die) and the probabilities are encoded by a discrete list of the probabilities of the outcomes; in this case the discrete probability distribution is known as probability mass function.
In probability theory and statistics, the beta distribution is a family of continuous probability distributions defined on the interval [0, 1] or (0, 1) in terms of two positive parameters, denoted by alpha (α) and beta (β), that appear as exponents of the variable and its complement to 1, respectively, and control the shape of the distribution.
Overdispersion occurs when there is more variability in the data than there should otherwise be expected according to the assumed distribution of the data. In summary, to ensure efficient inference of the regression parameters and the regression function, the heteroscedasticity must be accounted for.
A random deviate or simply deviate is the difference of a random variate with respect to the distribution central location (e.g., mean), often divided by the standard deviation of the distribution (i.e., as a standard score). [1] Random variates are used when simulating processes driven by random influences (stochastic processes).