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In mathematics, an average or central tendency of a set (list) of data refers to a measure of the "middle" of the data set. There are many different descriptive statistics that can be chosen as a measurement of the central tendency. The most common method, and the one generally referred to simply as the average, is the arithmetic mean. Please see the table of mathematical symbols for explanations of the symbols used. In statistics, the term central tendency is used in some fields of empirical research to refer to what statisticians sometimes call "location". A "measure of central tendency" is either a location parameter or a statistic used to estimate a location parameter.
A list of measures of central tendency There are several different kinds of calculations for central tendency, the kind of calculation that should be used depends on the type of data (level of measurement) and purpose for which the central tendency is being calculated: Other averages Other more sophisticated averages are: trimean, trimedian, and normalised mean, to name a few. These are usually more representative of the whole dataset. One can create one's own average metric using Generalised f-mean: where is any invertible function. For example, expmean (exponential mean) is a mean using the function , and it is inherently biased towards the higher values. The only significant reason why the arithmetic mean (classical average) is generally used in scientific papers is that there are various (statistical) tests which can be applied to test the statistical significance of the results, as well as the correlations that are explored through these metrics. Derivation of the name The original meaning of the word is "damage sustained at sea": the same word is found in Arabic as awar, in Italian as avaria and in French as avarie. Hence an average adjuster is a person who assesses an insurable loss. Marine damage is either particular average, which is borne only by the owner of the damaged property, or general average, where the owner can claim a proportional contribution from all the parties to the marine venture. The type of calculations used in adjusting general average gave rise to the use of "average" to mean "arithmetic mean". See also Further reading | ||||||||
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