Central tendency

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In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.wikipedia
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Statistics

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In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.
Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other.

Average

Rushing averageReceiving averagemean
Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.
In statistics, mean, median, and mode are all known as measures of central tendency, and in colloquial usage any of these might be called an average value.

Median

averagesample medianmedian-unbiased estimator
The most common measures of central tendency are the arithmetic mean, the median and the mode. Median: the middle value that separates the higher half from the lower half of the data set. The median and the mode are the only measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely.
The median is 2 in this case, (as is the mode), and it might be seen as a better indication of central tendency (less susceptible to the exceptionally large value in data) than the arithmetic mean of 4.

Arithmetic mean

meanaveragearithmetic
The most common measures of central tendency are the arithmetic mean, the median and the mode.
While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values).

Statistical dispersion

dispersionvariabilityspread
The central tendency of a distribution is typically contrasted with its dispersion or variability; dispersion and central tendency are the often characterized properties of distributions.
Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.

Level of measurement

quantitativescaleinterval scale
Median: the middle value that separates the higher half from the lower half of the data set. The median and the mode are the only measures of central tendency that can be used for ordinal data, in which values are ranked relative to each other but are not measured absolutely.
The mode, i.e. the most common item, is allowed as the measure of central tendency for the nominal type.

Interquartile mean

interquartile
Interquartile mean: a truncated mean based on data within the interquartile range.
The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range.

Mid-range

midsummarymidrangehalf-range
Midrange: the arithmetic mean of the maximum and minimum values of a data set.
The mid-range is the midpoint of the range; as such, it is a measure of central tendency.

Geometric median

minimizing the sum of distances
Geometric median: which minimizes the sum of distances to the data points. This is the same as the median when applied to one-dimensional data, but it is not the same as taking the median of each dimension independently. It is not invariant to different rescaling of the different dimensions.
This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions.

Winsorized mean

Winsorized mean: an arithmetic mean in which extreme values are replaced by values closer to the median.
A winsorized mean is a winsorized statistical measure of central tendency, much like the mean and median, and even more similar to the truncated mean.

Simplicial depth

Simplicial depth: the probability that a randomly chosen simplex with vertices from the given distribution will contain the given center
In robust statistics and computational geometry, simplicial depth is a measure of central tendency determined by the simplices that contain a given point.

Mode (statistics)

modemodalmodes
The most common measures of central tendency are the arithmetic mean, the median and the mode.
Central tendency

Interquartile range

inter-quartile rangebelowinterquartile
Interquartile mean: a truncated mean based on data within the interquartile range.
The median is the corresponding measure of central tendency.

Lp space

L'' ''p'' spaceL ''p'' spacesL'' ''p'' spaces
In the sense of L p spaces, the correspondence is:
In statistics, measures of central tendency and statistical dispersion, such as the mean, median, and standard deviation, are defined in terms of L p metrics, and measures of central tendency can be characterized as solutions to variational problems.

Weighted arithmetic mean

averageaverage ratingweighted average
Weighted arithmetic mean: an arithmetic mean that incorporates weighting to certain data elements.
Central tendency

Mean

mean valuepopulation meanaverage
In probability and statistics, the population mean, or expected value, are a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.

Average absolute deviation

mean absolute deviationmean deviationMAD
In this general form, the central point can be the mean, median, mode, or the result of another measure of central tendency.

Deviation (statistics)

deviationabsolute deviationdeviations
Typically the deviation is reckoned from the central value, being construed as some type of average, most often the median or sometimes the mean of the data set.

Calculus of variations

variationalvariational calculusvariational methods
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.
Measures of central tendency as solutions to variational problems

Location parameter

locationlocation modelshift parameter
Location parameter
Central tendency

Probability distribution

distributioncontinuous probability distributiondiscrete probability distribution
In statistics, a central tendency (or measure of central tendency) is a central or typical value for a probability distribution.

Normal distribution

normally distributednormalGaussian
A central tendency can be calculated for either a finite set of values or for a theoretical distribution, such as the normal distribution.

Data

statistical datascientific datadatum
Occasionally authors use central tendency to denote "the tendency of quantitative data to cluster around some central value."

Geometric mean

geometric averagegeometricmean
Geometric mean: the nth root of the product of the data values, where there are n of these. This measure is valid only for data that are measured absolutely on a strictly positive scale.