Originally, the word average referred to "financial loss from goods being damaged in transit". This might seem very distant from the modern definition, but the connection is that anyone who invested in a ship with lost/damaged goods (or their insurers) had to turn in the average value of the damage. So, for a while, "average" meant "equal sharing of loss", and by 1755 the word took on its current mathematical connotation. Average was borrowed in the late 1400s from French avarie, which referred to ship damage in general. Beyond that, there are many possible explanations for the etymology; in fact, it's one of the most investigated origins, to no avail. It might be from Arabic awar, meaning "defect", Latin habere, meaning "to have", or various other linguistic permutations.
Hello! I'm Adam Aleksic. This year, I graduated from Harvard University with a degree in Government and Linguistics. There, I co-founded the Harvard Undergraduate Linguistics Society and wrote a thesis on Serbo-Croatian language policy, magna cum laude. In addition to etymology, I also really enjoy philosophy, trivia, vexillology, geography, board games, conlanging, art history, and law.