Editing Average (section)

===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 Unpublished presidential address, American Statistical Association, 131st Annual Meeting, Fort Collins, Colorado. 1971.]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.