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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 ...
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 ...
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 ...
A moderately robust measure of central tendency - known as the decile mean - can be computed by making use of a sample's deciles to (= 10th percentile, = 20th percentile and so on). It is calculated as follows: [3]
The most widely encountered probability distribution is called the normal distribution; it has the property that all measures of its central tendency, including not just the mean but also the median mentioned above and the mode (the three Ms [7]), are equal. This equality does not hold for other probability distributions, as illustrated for the ...
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.
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 ...
The geometric mean and the harmonic mean are allowed to measure the central tendency, in addition to the mode, median, and arithmetic mean. The studentized range and the coefficient of variation are allowed to measure statistical dispersion. All statistical measures are allowed because all necessary mathematical operations are defined for the ...
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