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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.
Some measures that are commonly used to describe a data set are measures of central tendency and measures of variability or dispersion. Measures of central tendency include the mean, median and mode, while measures of variability include the standard deviation (or variance), the minimum and maximum values of the variables, kurtosis and skewness ...
Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or .
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. It is defined as the ratio of the standard deviation to the ...
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 " true value ") are called ...
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution. [1] Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s. [2] The most common measures of central tendency are the arithmetic mean, the median, and ...
In descriptive statistics, the interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the data. [1] The IQR may also be called the midspread, middle 50%, fourth spread, or H‑spread. It is defined as the difference between the 75th and 25th percentiles of the data. [2][3][4] To calculate the IQR, the data set ...
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 ...