# Category: Means

Mean operation
In algebraic topology, a mean or mean operation on a topological space X is a continuous, commutative, idempotent binary operation on X. If the operation is also associative, it defines a semilattice.
Mode (statistics)
The mode is the value that appears most often in a set of data values. If X is a discrete random variable, the mode is the value x (i.e, X = x) at which the probability mass function takes its maximum
Mean square
In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. It may also be defined as the arithmetic mea
Average
In ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list (the arithmetic mean). For
Quasi-arithmetic mean
In mathematics and statistics, the quasi-arithmetic mean or generalised f-mean is one generalisation of the more familiar means such as the arithmetic mean and the geometric mean, using a function . I
Power mean
No description available.
Interquartile mean
The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range. The IQM is very similar to the scoring method used in spo
Generalized f-mean
No description available.
Mean
There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a gi
Lehmer mean
In mathematics, the Lehmer mean of a tuple of positive real numbers, named after Derrick Henry Lehmer, is defined as: The weighted Lehmer mean with respect to a tuple of positive weights is defined as
Mid-range
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: The mid-range is closely rela
Winsorized mean
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. It involves the calculation of the mean after win
In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means.
Geometric mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their
Inequality of arithmetic and geometric means
In mathematics, the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers is greater than or equal
Centerpoint (geometry)
In statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher-dimensional Euclidean space. Given a set of points in d-dimensional space, a cen
Chisini mean
In mathematics, a function f of n variables x1, ..., xn leads to a Chisini mean M if for every vector , there exists a unique M such that f(M,M, ..., M) = f(x1,x2, ..., xn). The arithmeti
Midhinge
In statistics, the midhinge is the average of the first and third quartiles and is thus a measure of location.Equivalently, it is the 25% trimmed mid-range or 25% midsummary; it is an L-estimator. The
Circular mean
In mathematics and statistics, a circular mean or angular mean is a mean designed for angles and similar cyclic quantities, such as daytimes, and fractional parts of real numbers. This is necessary si
Identric mean
The identric mean of two positive real numbers x, y is defined as: It can be derived from the mean value theorem by considering the secant of the graph of the function . It can be generalized to more
Contraharmonic mean
In mathematics, a contraharmonic mean is a function complementary to the harmonic mean. The contraharmonic mean is a special case of the Lehmer mean, , where p = 2.
Logarithmic mean
In mathematics, the logarithmic mean is a function of two non-negative numbers which is equal to their difference divided by the logarithm of their quotient. This calculation is applicable in engineer
Median
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be th
Modified mean
No description available.
Weighted geometric mean
In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. Given a sample and weights , it is calculated as: The second form above illustr
Harmonic mean
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired. The
Pythagorean means
In mathematics, the three classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions by Pythagoreans and l
Root mean square
In mathematics and its applications, the root mean square of a set of numbers (abbreviated as RMS, RMS or rms and denoted in formulas as either or ) is defined as the square root of the mean square (t
Weighted median
In statistics, a weighted median of a sample is the 50% weighted percentile. It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust
Fréchet mean
In mathematics and statistics, the Fréchet mean is a generalization of centroids to metric spaces, giving a single representative point or central tendency for a cluster of points. It is named after M
Truncated mean
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 dist
Assumed mean
In statistics the assumed mean is a method for calculating the arithmetic mean and standard deviation of a data set. It simplifies calculating accurate values by hand. Its interest today is chiefly hi
Arithmetic–geometric mean
In mathematics, the arithmetic–geometric mean of two positive real numbers x and y is defined as follows: Call x and y a0 and g0: Then define the two interdependent sequences (an) and (gn) as These tw
Mean signed deviation
In statistics, the mean signed difference (MSD), also known as mean signed deviation and mean signed error, is a sample statistic that summarises how well a set of estimates match the quantities that
Medoid
Medoids are representative objects of a data set or a cluster within a data set whose sum of dissimilarities to all the objects in the cluster is minimal. Medoids are similar in concept to means or ce
Trimean
In statistics the trimean (TM), or Tukey's trimean, is a measure of a probability distribution's location defined as a weighted average of the distribution's median and its two quartiles: This is equi
Riesz mean
In mathematics, the Riesz mean is a certain mean of the terms in a series. They were introduced by Marcel Riesz in 1911 as an improvement over the Cesàro mean. The Riesz mean should not be confused wi
Pseudomedian
In statistics, the pseudomedian is a measure of centrality for data-sets and populations. It agrees with the median for symmetric data-sets or populations. In mathematical statistics, the pseudomedian
Mean of a function
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over th
Spherical mean
In mathematics, the spherical mean of a function around a point is the average of all values of that function on a sphere of given radius centered at that point.
Bochner–Riesz mean
The Bochner–Riesz mean is a summability method often used in harmonic analysis when considering convergence of Fourier series and Fourier integrals. It was introduced by Salomon Bochner as a modificat
Tukey median
No description available.
Neuman–Sándor mean
In mathematics of special functions, the Neuman–Sándor mean M, of two positive and unequal numbers a and b, is defined as: This mean interpolates the inequality of the unweighted arithmetic mean A = (
Heinz mean
In mathematics, the Heinz mean (named after E. Heinz) of two non-negative real numbers A and B, was defined by Bhatia as: with 0 ≤ x ≤ 1/2. For different values of x, this Heinz mean interpolates betw
Stolarsky mean
In mathematics, the Stolarsky mean is a generalization of the logarithmic mean. It was introduced by in 1975.
Temporal mean
The temporal mean is the arithmetic mean of a series of values over a time period. Assuming equidistant measuring or sampling times, it can be computed as the sum of the values over a period divided b
Arithmetic mean
In mathematics and statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk ˈmiːn/ air-ith-MET-ik) or arithmetic average, or just the mean or the average (when the context is clear), is the sum of a collection
Geometric–harmonic mean
In mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0 = x and h0 = y and call it g1, i.e. g1 is the square ro
Weighted arithmetic mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some
Subcontrary mean
No description available.
Cubic mean
The cubic mean (written as ) is a specific instance of the generalized mean with .
Grand mean
The grand mean or pooled mean is the average of the means of several subsamples, as long as the subsamples have the same number of data points. For example, consider several lots, each containing seve
Heronian mean
In mathematics, the Heronian mean H of two non-negative real numbers A and B is given by the formula: It is named after Hero of Alexandria.
Centroid
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the
Generalized mean
In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means (arith
Cesàro summation
In mathematical analysis, Cesàro summation (also known as the Cesàro mean) assigns values to some infinite sums that are not necessarily convergent in the usual sense. The Cesàro sum is defined as the
Geometric median
In geometry, the geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the