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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 mean may be confused with the median, mode or mid-range, as any of these may incorrectly be called an "average" (more formally, a measure of central tendency). The mean of a set of observations is the arithmetic average of the values; however, for skewed distributions , the mean is not necessarily the same as the ...
In statistics, the mid-range or mid-extreme is a measure of central tendency of a sample defined as the arithmetic mean of the maximum and minimum values of the data set: [1] M = max x + min x 2 . {\displaystyle M={\frac {\max x+\min x}{2}}.}
For example, per capita income is the arithmetic average income of a nation's population. While the arithmetic mean is often used to report central tendencies , it is not a robust statistic : it is greatly influenced by outliers (values much larger or smaller than most others).
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).
In probability theory and statistics, a central moment is a moment of a probability distribution of a random variable about the random variable's mean; that is, it is the expected value of a specified integer power of the deviation of the random variable from the mean. The various moments form one set of values by which the properties of a ...
Measures of spatial central tendency [ edit ] The coordinate-wise mean of a point set is the centroid , which solves the same variational problem in the plane (or higher-dimensional Euclidean space ) that the familiar average solves on the real line — that is, the centroid has the smallest possible average squared distance to all points in ...
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median. It involves the calculation of the mean after discarding given parts of a probability distribution or sample at the high and low end, and typically discarding an equal amount of both. This number of points to be discarded is usually ...