The most ordinary word in statistics started out on a ship in trouble at sea.
In the maritime trade of the 12th-century Mediterranean, Italian avaria and French avarie meant damage to a ship or its cargo. Spanish had averia, and Dutch and German later borrowed their own forms. Where the Romance word came from is less clear. Some trace it to Arabic 'awariya, "damaged merchandise," and Wikipedia gives that as the source. Etymonline calls the word "of uncertain origin" and quotes the OED: "Few words have received more etymological investigation."
English took the word in the late 1400s as a merchant's term. It first meant a small charge, beyond the freight cost, that owners of goods paid to a ship's master. It also meant the financial loss from goods damaged in transit.
The key shift came from an old rule of the sea, now called general average. If a crew threw cargo overboard to save a ship in a storm, the loss was not left with the unlucky owner. Everyone with a stake in the voyage paid a share in proportion to what they had aboard. A Roman jurist, Julius Paulus, put it around AD 230: "the loss is made good by the assessment of all which is made for the benefit of all."
Once "average" meant that fair sharing out, it was a short step to arithmetic. Etymonline dates the sense of a "medial estimate" to 1735 and the arithmetic mean to 1755. The adjective arrived in 1770, and by 1803 it could mean the mean of a set. The meaning "of medium character," ordinary, followed after that.
The maritime sense never died. Shipowners still declare general average, and they did so after the Ever Given blocked the Suez Canal in 2021. The rule that gave statistics its basic word is still being applied to cargo.