Mean

In statistics, mean has two related meanings:

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• the average in ordinary English, which is more correctly called the arithmetic mean, to distinguish it from geometric mean or harmonic mean. The average is also called sample mean.
• the expected value of a random variable, which is also called the population mean.

As well as statistics, means are often used in geometry and analysis; a wide range of means have been developed for these purposes, which are not much used in statistics. See the Other means section below for a list of means.

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Sample mean is often used as an estimator of the central tendency such as the population mean. However, other estimators are also used. For example, the median is a more robust estimator of the central tendency than the sample mean.

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For a real-valued random variable X, the mean is the expectation of X.

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If the expectation does not exist, then the random variable has no mean.

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For a data set, the mean is just the sum of all the observations divided by the number of observations.

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Once we have chosen this method of describing the communality of a data set, we usually use the standard deviation to describe how the observations differ.

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The standard deviation is the square root of the average of squared deviations from the mean.

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The mean is the unique value about which the sum of squared deviations is a minimum.

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If you calculate the sum of squared deviations from any other measure of central tendency, it will be larger than for the mean.

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This explains why the standard deviation and the mean are usually cited together in statistical reports.

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An alternative measure of dispersion is the mean deviation, equivalent to the average absolute deviation from the mean. It is less sensitive to outliers, but less tractable when combining data sets.

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The mean value of a function, f(x), on an interval, a

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:E(f(X))=rac{int_a^b f(x),dx}{b-a}.

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Note that not every probability distribution has a defined mean or variance — see the Cauchy distribution for an example.

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The following is a summary of some of the multiple methods for calculating the mean of a set of n numbers. See the table of mathematical symbols for explanations of the symbols used.

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Mean: Arithmetic mean ►



 

Estimator: In statistics, an estimator is a function of the known sample data that is used to estimate an unknown population parameter; an estimate is the result from the actual application of the function to a particular set of data. Many different estimators are possible for any given parameter. Some criteri...

Central tendency: In statistics, central tendency is an average of a set of measurements, the word average being variously construed as mean, median, or other measure of location, depending on the context. Central tendency is a descriptive statistic analogous to center of mass in physical terms. The term is used in...

Median: :This article is about the statistical concept, for alternative meanings see median (disambiguation)....




Mean related Images and Photos (experimental)

Mean Creek	Mean Creek	Mean Girls	Mean Machine
Mean Streets	Mean Streets	Mean Streets	Mean Collection 1891
TapouT Mean Girls Womens T-Shirt	Mean Streets Italian Movie Poster 1973	You Mean Whales are Even Bigger?	Jerry Lee Lewis - Mean Old Man CD