From Arabic 'ʿawārīya' (damaged goods) — the math sense arose because sea-cargo losses were split proportionally among merchants.
A number expressing the central or typical value in a set of data; also, the ordinary or typical level.
From French 'avarie' (damage to a ship or cargo), from Italian 'avaria,' from Arabic 'ʿawārīya' (عوارية), meaning 'damaged goods,' derived from 'ʿawār' (عوار, defect, damage). The mathematical sense arose from maritime insurance: when cargo was damaged at sea, the financial loss was distributed proportionally among all merchants with goods aboard -- this proportional sharing of loss was called 'average,' and the arithmetic required to calculate each merchant's share gave birth to the mathematical meaning. Key roots: ʿawār (Arabic: "defect
In maritime law, 'general average' is still a living legal principle: if cargo must be jettisoned to save a ship, all cargo owners share the loss proportionally. This centuries-old practice of dividing damage equally is literally why we call a middle value an 'average' -- the mathematical concept was born from splitting shipping losses.