Editing Average (section)

==History==

===Origin===
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.<ref name="ReferenceA">{{cite journal |doi=10.2307/2333051 | volume=45 | issue=1/2 | title=Studies in the History of Probability and Statistics: VII. The Principle of the Arithmetic Mean | journal=Biometrika | pages=130–135| jstor=2333051 |date=1958 | last1=Plackett | first1=R. L. }}</ref><ref name="york.ac.uk">[http://www.york.ac.uk/depts/maths/histstat/eisenhart.pdf Eisenhart, Churchill. "The development of the concept of the best mean of a set of measurements from antiquity to the present day." Unpublished presidential address, American Statistical Association, 131st Annual Meeting, Fort Collins, Colorado. 1971.]</ref> 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. Using the mean of several measured values, scientists assumed that the errors add up to a relatively small number when compared to the total of all measured values. The method of taking the mean for reducing observation errors was indeed mainly developed in astronomy.<ref name="ReferenceA"/><ref name="amstatbakker">{{Cite web |url=http://www.amstat.org/publications/jse/v11n1/bakker.html |title=Bakker, Arthur. "The early history of average values and implications for education." Journal of Statistics Education 11.1 (2003): 17-26. |access-date=2015-10-22 |archive-date=2015-12-04 |archive-url=https://web.archive.org/web/20151204181338/http://www.amstat.org/publications/jse/v11n1/bakker.html |url-status=live }}</ref> A possible precursor to the arithmetic mean is the [[mid-range]] (the mean of the two extreme values), used for example in Arabian astronomy of the ninth to eleventh centuries, but also in metallurgy and navigation.<ref name="york.ac.uk"/>

However, there are various older vague references to the use of the arithmetic mean (which are not as clear, but might reasonably have to do with our modern definition of the mean). In a text from the 4th century, it was written that (text in square brackets is a possible missing text that might clarify the meaning):<ref>{{Cite web |url=https://arcaneknowledgeofthedeep.files.wordpress.com/2014/02/theologyarithmetic.pdf |title=Waterfield, Robin. "The theology of arithmetic." On the Mystical, mathematical and Cosmological Symbolism of the First Ten Number (1988). page 70. |access-date=2018-11-27 |archive-url=https://web.archive.org/web/20160304212935/https://arcaneknowledgeofthedeep.files.wordpress.com/2014/02/theologyarithmetic.pdf |archive-date=2016-03-04 |url-status=dead }}</ref>
: In the first place, we must set out in a row the sequence of numbers from the monad up to nine: 1, 2, 3, 4, 5, 6, 7, 8, 9. Then we must add up the amount of all of them together, and since the row contains nine terms, we must look for the ninth part of the total to see if it is already naturally present among the numbers in the row; and we will find that the property of being [one] ninth [of the sum] only belongs to the [arithmetic] mean itself...

Even older potential references exist. There are records that from about 700 BC, merchants and shippers agreed that damage to the cargo and ship (their "contribution" in case of damage by the sea) should be shared equally among themselves.<ref name="amstatbakker"/> This might have been calculated using the average, although there seem to be no direct record of the calculation.

===Etymology===
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".{{Efn|1=Medieval [[Arabic]] had عور ''ʿawr'' meaning "blind in one eye" and عوار ''ʿawār'' meant "any defect, or anything defective or damaged". Some medieval [[Arabic]] dictionaries are at [http://www.baheth.info/ Baheth.info] {{Webarchive |url=https://web.archive.org/web/20131029192325/http://www.baheth.info/ |date=2013-10-29 }}, and some translation to English of what's in the medieval [[Arabic]] dictionaries is in [http://dict.yulghun.com/lane/ Lane's ''Arabic-English Lexicon'', pages 2193 and 2195]. The medieval dictionaries do not list the word-form عوارية ''ʿawārīa''. ''ʿAwārīa'' can be naturally formed in [[Arabic]] grammar to refer to things that have ''ʿawār'', but in practice in medieval [[Arabic]] texts ''ʿawārīa'' is a rarity or non-existent, while the forms عواري ''ʿawārī'' and عوارة ''ʿawāra'' are frequently used when referring to things that have ''ʿawār'' or damage – this can be seen in the searchable collection of medieval texts at [http://www.alwaraq.net/Core/SearchServlet/searchall?book=-1&option=1&offset=1&searchtext=2LnZiNin2LHZig==&WordForm=1&RangeOp=-1 AlWaraq.net] (book links are clickable on righthand side).}} Within the Western languages the word's history begins in medieval sea-commerce on the Mediterranean. 12th and 13th century Genoa Latin ''avaria'' meant "damage, loss and non-normal expenses arising in connection with a merchant sea voyage"; and the same meaning for ''avaria'' is in Marseille in 1210, Barcelona in 1258 and Florence in the late 13th.{{Efn|name=Avaria|1=The [[Arabic]] origin of ''avaria'' was first reported by Reinhart Dozy in the 19th century. Dozy's original summary is in his 1869 book [https://archive.org/stream/glossairedesmot00englgoog#page/n235/mode/1up ''Glossaire'']. Summary information about the word's early records in Italian-Latin, Italian, Catalan, and French is at [http://www.cnrtl.fr/definition/avarie ''avarie'' @ CNRTL.fr] {{Webarchive |url=https://web.archive.org/web/20190106172304/http://www.cnrtl.fr/definition/avarie |date=2019-01-06 }}. The seaport of Genoa is the location of the earliest-known record in European languages, year 1157. A set of medieval Latin records of ''avaria'' at Genoa is in the downloadable lexicon [http://www.storiapatriasavona.it/vocabolario-ligure/ ''Vocabolario Ligure''], by Sergio Aprosio, year 2001, ''avaria'' in Volume 1 pages 115-116. Many more records in medieval Latin at Genoa are at [http://StoriaPatriaGenova.it StoriaPatriaGenova.it], usually in the plurals ''avariis'' and ''avarias''. At the port of Marseille in the 1st half of the 13th century notarized commercial contracts have dozens of instances of Latin ''avariis'' (ablative plural of ''avaria''), as published in [https://archive.org/details/documentsindit01blan Blancard year 1884]. Some information about the English word over the centuries is at [https://archive.org/stream/oed01arch#page/582/mode/1up NED (year 1888)]. See also the definition of English "average" in English dictionaries published in the early 18th century, i.e., in the time period just before the big transformation of the meaning: [https://books.google.com/books?id=PHBUAAAAYAAJ&pg=PT71&dq=dammage%20cargo%20goods Kersey-Phillips' dictionary (1706)], [https://archive.org/stream/glossographiaan00blougoog#page/n64/mode/1up Blount's dictionary (1707 edition)], [https://archive.org/stream/merchantsmagazi00hattgoog#page/n275/mode/1up Hatton's dictionary (1712)], [https://archive.org/stream/universaletymolo00bailuoft#page/n89/mode/1up Bailey's dictionary (1726)], [https://books.google.com/books?id=e-U_AQAAMAAJ&pg=PA120 Martin's dictionary (1749)]. Some complexities surrounding the English word's history are discussed in [https://archive.org/stream/contestedetymolo00wedgiala#page/10/mode/2up Hensleigh Wedgwood year 1882 page 11] and [https://archive.org/stream/etymologicaldict00skeauoft#page/781/mode/1up Walter Skeat year 1888 page 781]. Today there is consensus that: (#1) today's English "average" descends from medieval Italian ''avaria'', Catalan ''avaria'', and (#2) among the Latins the word ''avaria'' started in the 12th century and it started as a term of Mediterranean sea-commerce, and (#3) there is no root for ''avaria'' to be found in Latin, and (#4) a substantial number of Arabic words entered Italian, Catalan and Provençal in the 12th and 13th centuries starting as terms of Mediterranean sea-commerce, and (#5) the Arabic ''ʿawār {{!}} ʿawārī'' is phonetically a good match for ''avaria'', as conversion of w to v was regular in Latin and Italian, and ''-ia'' is a suffix in Italian, and the Western word's earliest records are in Italian-speaking locales (writing in Latin). And most commentators agree that (#6) the Arabic ''ʿawār {{!}} ʿawārī'' = "damage {{!}} relating to damage" is semantically a good match for ''avaria'' = "damage or damage expenses". A minority of commentators have been dubious about this on the grounds that the early records of Italian-Latin ''avaria'' have, in some cases, a meaning of "an expense" in a more general sense – [http://tlio.ovi.cnr.it/voci/005020.htm see TLIO (in Italian)]. The majority view is that the meaning of "an expense" was an expansion from "damage and damage expense", and the chronological order of the meanings in the records supports this view, and the broad meaning "an expense" was never the most commonly used meaning. On the basis of the above points, the inferential step is made that the Latinate word came or probably came from the Arabic word.}} 15th-century [[French language|French]] ''avarie'' had the same meaning, and it begot [[English language|English]] "averay" (1491) and English "average" (1502) with the same meaning. Today, Italian ''avaria'', Catalan ''avaria'' and French ''avarie'' still have the primary meaning of "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. Today's meaning developed out of that, and started in the mid-18th century, and started in English.{{Efn|name=Avaria}}<ref>{{Cite Dictionary.com |average |access-date=2023-05-25 }}</ref>

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".

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 animal]]s ("avers").<ref>{{cite book |last=Ray |first=John |author-link=John Ray |title=A Collection of English Words not Generally Used |date=1674 |publisher=H. Bruges |location=London |url=http://babel.hathitrust.org/cgi/pt?id=njp.32101037601729;view=1up;seq=19 |access-date=18 May 2015}}</ref>

There is earlier (from at least the 11th century), unrelated use of the word. 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.<ref>{{cite OED |term=average, n.2 |date=September 2019 |id=13681 |access-date=September 5, 2019 }}</ref>