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Several measures of central tendency can be characterized as solving a variational problem, in the sense of the calculus of variations, namely minimizing variation from the center. That is, given a measure of statistical dispersion, one asks for a measure of central tendency that minimizes variation: such that variation from the center is ...
The center can be found using the Floyd–Warshall algorithm. [4] [5] Another algorithm has been proposed based on matrix calculus. [6] The concept of the center of a graph is related to the closeness centrality measure in social network analysis, which is the reciprocal of the mean of the distances d(A,B). [1]
[7] Some have alleged that departures in normality in the process output significantly reduce the effectiveness of the charts to the point where it may require control limits to be set based on percentiles of the empirically-determined distribution of the process output [2]: 237 although this assertion has been consistently refuted. See Footnote 6.
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. [1] There are several kinds of means (or "measures of central tendency") in mathematics, especially in statistics.
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 ...
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 ...
The two measures are complementary in sense that if one knows the mid-range and the range, one can find the sample maximum and minimum values. The mid-range is rarely used in practical statistical analysis, as it lacks efficiency as an estimator for most distributions of interest, because it ignores all intermediate points, and lacks robustness ...
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]