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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 .
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 is divided into quartiles , or four rank-ordered even parts via linear interpolation. [ 1 ]
It is calculated as the difference between the largest and smallest values (also known as the sample maximum and minimum). [1] It is expressed in the same units as the data. The range provides an indication of statistical dispersion. Since it only depends on two of the observations, it is most useful in representing the dispersion of small data ...
[1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [ 3 ] For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads , and ...
Example of samples from two populations with the same mean but different standard deviations. Red population has mean 100 and SD 10; blue population has mean 100 and SD 50. A large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.
In mathematics, and especially in category theory, a commutative diagram is a diagram of objects, also known as vertices, and morphisms, also known as arrows or edges, such that when selecting two objects any directed path through the diagram leads to the same result by composition.
The term was coined when variables began to be used for sets and mathematical structures. onto A function (which in mathematics is generally defined as mapping the elements of one set A to elements of another B) is called "A onto B" (instead of "A to B" or "A into B") only if it is surjective; it may even be said that "f is onto" (i. e ...
Definitions of the appropriate topologies on spaces of test functions and distributions are given in the article on spaces of test functions and distributions. This article is primarily concerned with the definition of distributions, together with their properties and some important examples.