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# Average

In colloquial language, an average is a middle or typical number of a list of numbers. [1]

## Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

## Average

In colloquial language, an average is a middle or typical number of a list of numbers.

## Average absolute deviation

The average absolute deviation (or mean absolute deviation) of a data set is the average of the absolute deviations from a central point.

## Central limit theorem

In probability theory, the central limit theorem (CLT) establishes that, in some situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed.

## Central tendency

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

## Colloquialism

Everyday language, everyday speech, common parlance, informal language, colloquial language, general parlance, or vernacular (but this has other meanings too), is the most used variety of a language, which is usually employed in conversation or other communication in informal situations.

## Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

## Cubic mean

The cubic mean \bar_\mathrm of n real numbers x_i \in \mathbb R is defined as.

## Descriptive statistics

A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics.

## Digital filter

In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal.

## Digital signal processing

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations.

## Domesday Book

Domesday Book (or; Latin: Liber de Wintonia "Book of Winchester") is a manuscript record of the "Great Survey" of much of England and parts of Wales completed in 1086 by order of King William the Conqueror.

## Estimation

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable.

## Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

## General average

The law of general average is a legal principle of maritime law according to which all parties in a sea venture proportionally share any losses resulting from a voluntary sacrifice of part of the ship or cargo to save the whole in an emergency (for instance, when the crew throws some cargo overboard to lighten the ship in a storm).

## Generalized mean

In mathematics, generalized means are a family of functions for aggregating sets of numbers, that include as special cases the Pythagorean means (arithmetic, geometric, and harmonic means).

## Geometric mean

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).

## Geometric median

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.

## Glasgow Mathematical Journal

The Glasgow Mathematical Journal is a mathematics journal that publishes original research papers in any branch of pure and applied mathematics.

## Harmonic mean

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.

## 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 to the geometric mean of the same list; and further, that the two means are equal if and only if every number in the list is the same.

## Interquartile mean

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

## Interquartile range

In descriptive statistics, the interquartile range (IQR), also called the midspread or middle 50%, or technically H-spread, is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR.

## Invariant (mathematics)

In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.

## Law of averages

The law of averages is the law that a particular outcome or event is inevitable or certain simply because it is statistically possible.

## List of mathematical symbols

This is a list of symbols used in all branches of mathematics to express a formula or to represent a constant.

## Log-normal distribution

In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Mean

In mathematics, mean has several different definitions depending on the context.

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## Measurement

Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

## Median

The median is the value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

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## Mid-range

In statistics, the mid-range or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as: The mid-range is the midpoint of the range; as such, it is a measure of central tendency.

## Mode (statistics)

The mode of a set of data values is the value that appears most often.

## Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

## Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

## 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 f. It is also called Kolmogorov mean after Russian mathematician Andrey Kolmogorov.

## Root mean square

In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of the mean square (the arithmetic mean of the squares of a set of numbers).

## Rotation (mathematics)

Rotation in mathematics is a concept originating in geometry.

## Skewness

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean.

## Summation

In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.

## Time series

A time series is a series of data points indexed (or listed or graphed) in time order.

## 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 equivalent to the average of the median and the midhinge: The foundations of the trimean were part of Arthur Bowley's teachings, and later popularized by statistician John Tukey in his 1977 book which has given its name to a set of techniques called exploratory data analysis.

## Truncated mean

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

## 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 data points contribute more than others.

## 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.

## Working animal

A working animal is an animal, usually domesticated, that is kept by humans and trained to perform tasks.

## References

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