Average

In ordinary language, an average is a single number or value that best represents a set of data.

Depending on the context, the most representative statistic to be taken as the average might be another measure of central tendency, such as the mid-range, median, mode or geometric mean.

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

[further explanation needed] Other more sophisticated averages are: trimean, trimedian, and normalized mean, with their generalizations.

The function g(x1, x2, ..., xn) = x1x2···xn (where the list elements are positive numbers) provides the geometric mean.

The function g(x1, x2, ..., xn) = (x1−1+x2−1+ ··· + xn−1)−1) (where the list elements are positive numbers) provides the harmonic mean.

The first recorded time that the arithmetic mean was extended from 2 to n cases for the use of estimation was in the sixteenth century.

From the late sixteenth century onwards, it gradually became a common method to use for reducing errors of measurement in various areas.

[5][6] At the time, astronomers wanted to know a real value from noisy measurement, such as the position of a planet or the diameter of the moon.

The root is found in Arabic as عوار ʿawār, a defect, or anything defective or damaged, including partially spoiled merchandise; and عواري ʿawārī (also عوارة ʿawāra) = "of or relating to ʿawār, a state of partial damage".

The huge transformation of the meaning in English began with the practice in later medieval and early modern Western merchant-marine law contracts under which if the ship met a bad storm and some of the goods had to be thrown overboard to make the ship lighter and safer, then all merchants whose goods were on the ship were to suffer proportionately (and not whoever's goods were thrown overboard); and more generally there was to be proportionate distribution of any avaria.

From there the word was adopted by British insurers, creditors, and merchants for talking about their losses as being spread across their whole portfolio of assets and having a mean proportion.

A second English usage, documented as early as 1674 and sometimes spelled "averish", is as the residue and second growth of field crops, which were considered suited to consumption by draught animals ("avers").

It appears to be an old legal term for a tenant's day labour obligation to a sheriff, probably anglicised from "avera" found in the English Domesday Book (1085).

The Oxford English Dictionary, however, says that derivations from German hafen haven, and Arabic ʿawâr loss, damage, have been "quite disposed of" and the word has a Romance origin.

[11] Due to the aforementioned colloquial nature of the term "average", the term can be used to obfuscate the true meaning of data and suggest varying answers to questions based on the averaging method (most frequently arithmetic mean, median, or mode) used.

[12] However, due to their persuasive power, averages and other statistical values should not be discarded completely, but instead used and interpreted with caution.

"[12] In many cases, data and specific calculations are provided to help facilitate this audience-based interpretation.