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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] A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set ...
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 ...
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when and , and it is described by this probability density function (or density): The variable has a mean of 0 and a variance and standard deviation of 1.
The coefficient of variation (CV) is defined as the ratio of the standard deviation to the mean , [1] It shows the extent of variability in relation to the mean of the population. The coefficient of variation should be computed only for data measured on scales that have a meaningful zero (ratio scale) and hence allow relative comparison of two ...
The standard deviation and the expected absolute deviation can both be used as an indicator of the "spread" of a distribution. The standard deviation is more amenable to algebraic manipulation than the expected absolute deviation, and, together with variance and its generalization covariance, is used frequently in theoretical statistics ...
Deviance (statistics) In statistics, deviance is a goodness-of-fit statistic for a statistical model; it is often used for statistical hypothesis testing. It is a generalization of the idea of using the sum of squares of residuals (SSR) in ordinary least squares to cases where model-fitting is achieved by maximum likelihood.
In another usage in statistics, normalization refers to the creation of shifted and scaled versions of statistics, where the intention is that these normalized values allow the comparison of corresponding normalized values for different datasets in a way that eliminates the effects of certain gross influences, as in an anomaly time series.
Deviation (statistics) Plot of standard deviation of a random distribution. In mathematics and statistics, deviation serves as a measure to quantify the disparity between an observed value of a variable and another designated value, frequently the mean of that variable. Deviations with respect to the sample mean and the population mean (or ...