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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.
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 ...
In statistics, the quartile coefficient of dispersion (QCD) is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation .
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution.
m(X) is the chosen measure of central tendency of the data set—sometimes the mean (¯), but most often the median. The average absolute deviation (AAD) in statistics is a measure of the dispersion or spread of a set of data points around a central value, usually the mean or median.
The median absolute deviation is a measure of statistical dispersion. Moreover, the MAD is a robust statistic, being more resilient to outliers in a data set than the standard deviation. In the standard deviation, the distances from the mean are squared, so large deviations are weighted more heavily, and thus outliers can heavily influence it ...
Several measures of statistical dispersion are defined in terms of the absolute deviation. The term "average absolute deviation" does not uniquely identify a measure of statistical dispersion, as there are several measures that can be used to measure absolute deviations, and there are several measures of central tendency that can be used as well.
Robust measures of scale can be used as estimators of properties of the population, either for parameter estimation or as estimators of their own expected value.. For example, robust estimators of scale are used to estimate the population standard deviation, generally by multiplying by a scale factor to make it an unbiased consistent estimator; see scale parameter: estimation.