Average

Rushing averageReceiving averagemeanaveragingrating averagearithmetic averagestatistical averageaveragesaverage valueaverage rating
In colloquial language, an average is a single number taken as representative of a list of numbers.wikipedia
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Arithmetic mean

meanaveragearithmetic
Often "average" refers to the arithmetic mean, the sum of the numbers divided by how many numbers are being averaged.
The term "arithmetic mean" is preferred in some contexts in mathematics and statistics because it helps distinguish it from other means, such as the geometric mean and the harmonic mean.

Mean

mean valueaveragepopulation mean
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. The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.
For a data set, the arithmetic mean, also called the mathematical expectation or average, is the central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values.

Central tendency

LocalityLocality (statistics)Measure of central tendency
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. The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.
Colloquially, measures of central tendency are often called averages. The term central tendency dates from the late 1920s.

Geometric mean

geometric averagegeometricmean
The geometric mean of n positive numbers is obtained by multiplying them all together and then taking the nth root.
In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

Harmonic mean

weighted harmonic meanharmonicHarmonically
Harmonic mean for a non-empty collection of numbers a 1, a 2, ..., a n, all different from 0, is defined as the reciprocal of the arithmetic mean of the reciprocals of the a i s:
In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

Descriptive statistics

descriptivedescriptive statisticstatistics
The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.
For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment or exposure group), and demographic or clinical characteristics such as the average age, the proportion of subjects of each sex, the proportion of subjects with related comorbidities, etc.

Truncated mean

trimmed meanModified meanOlympic average
A truncated mean or trimmed mean is a statistical measure of central tendency, much like the mean and median.

Trimean

Other more sophisticated averages are: trimean, trimedian, and normalized mean, with their generalizations.
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:

Weighted arithmetic mean

averageaverage ratingweighted average
More complicated forms involve using a weighted average.
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 data points contribute more than others.

Multiplicative calculus

Non-Newtonian calculusnon-Newtonian calculigeometric derivative
Furthermore, just as the arithmetic average (of functions) is the "natural" average in the classical calculus, the well-known geometric average is the "natural" average in the geometric calculus.

Generalized mean

power meanHölder meangeneralised

Colloquialism

colloquialcolloquiallycolloq.
In colloquial language, an average is a single number taken as representative of a list of numbers.

Statistics

statisticalstatistical analysisstatistician
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
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. The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.

Mode (statistics)

modemodalmodes
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. The mode, the median, and the mid-range are often used in addition to the mean as estimates of central tendency in descriptive statistics.

Measurement

measuremeasuringmeasurements
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.

Summation

sumsumssigma notation
If n numbers are given, each number denoted by a i (where i = 1,2, ..., n), the arithmetic mean is the sum of the as divided by n or

Logarithm

logarithmsloglogarithmic function
Geometric mean can be thought of as the antilog of the arithmetic mean of the logs of the numbers.

Multiplicative inverse

reciprocalinversereciprocals
Harmonic mean for a non-empty collection of numbers a 1, a 2, ..., a n, all different from 0, is defined as the reciprocal of the arithmetic mean of the reciprocals of the a i s:

Inequality of arithmetic and geometric means

AM–GM inequalityarithmetic-geometric mean inequalityAM-GM inequality
(The alphabetical order of the letters A, G, and H is preserved in the inequality.) See Inequality of arithmetic and geometric means.

List of mathematical symbols

Table of mathematical symbolsmathematical symbolsmathematical symbol
The table of mathematical symbols explains the symbols used below.

Geometric median

Weiszfeld's algorithmminimizing the sum of distances

Rotation (mathematics)

rotationrotationsrotate

Invariant (mathematics)

invariantinvariantsinvariance