Etymology
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average (n.)

late 15c., "any small charge over freight cost, payable by owners of goods to the master of a ship for his care of the goods," also "financial loss incurred through damage to goods in transit," from French avarie "damage to ship," and Italian avaria. A word from 12c. Mediterranean maritime trade (compare Spanish averia), of uncertain origin; sometimes traced to Arabic 'awariya "damaged merchandise." Dutch avarij, German haferei, etc., also are from Romanic languages. "Few words have received more etymological investigation" [OED].

Thus, when for the safety of a ship in distress any destruction of property is incurred, either by cutting away the masts, throwing goods overboard, or in other ways, all persons who have goods on board or property in the ship (or the insurers) contribute to the loss according to their average, that is, according to the proportionate value of the goods of each on board. [Century Dictionary]

The meaning developed to "equal sharing of loss by the interested parties." Transferred sense of "statement of a medial estimate, proportionate distribution of inequality among all," is first recorded 1735. The mathematical sense "a mean proportion arrived at by arithmetical calculation" is from 1755. Sports sense, of batting, attested by 1845, originally in cricket.

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average (adj.)
1770, "estimated by averaging," from average (n.). By 1803 as "equal in amount to the sum of all particular quantities divided by the number of them," hence "of medium character."
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average (v.)
1769, "to amount to," from average (n.). By 1831 as "find the arithmetical mean of unequal quantities;" 1914 as "divide among a number proportionately" (usually with out). Related: Averaged; averaging.
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e.r.a. (n.)
1949 in baseball as initialism (acronym) for earned run average. From 1971 in U.S. politics for Equal Rights Amendment.
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Joe 
pet-form of Joseph (q.v.). Meaning "generic fellow, man" is from 1846. Used in a wide range of invented names meaning "typical male example of," for example Joe college "typical college man" (1932); Joe Blow "average fellow" is U.S. military slang, first recorded 1941. "Dictionary of American Slang" lists, among other examples, Joe Average, Beige, Lunch Bucket, Public, Sad, Schmoe, Six-pack, Yale, Zilch
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John Q. Public (n.)
"imaginary average American citizen," 1934; the Q perhaps suggested by John Quincy Adams.
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outsized (adj.)

"larger than average," 1880, from out- + size. As a noun, "a person or thing larger than normal," 1845.

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batting (n.2)
"action of striking with a bat," 1610s, verbal noun from bat (v.2). In cricket, from 1773. Baseball batting average is from 1867.
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non-standard (adj.)

also nonstandard, "not average or usual," 1926, from non- + standard. A linguist's value-neutral term for language that is not of the form that is accepted as standard, which was formerly stigmatized as bad or vulgar.

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magna cum laude 

designating a diploma or degree of higher standard than average, by 1856, Latin, literally "with great praise;" from magna (see magnate) + cum laude.

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