'avg' originates as an abbreviation of the English word 'average', which ultimately comes into English via Old French.

'average' changed from Old French 'avarie' (related to Medieval Latin 'avaria') and eventually became the modern English word 'average'; the written abbreviation 'avg' developed in modern technical and statistical contexts (20th century onward).

Initially 'avarie' meant 'damage or loss (to a ship's cargo)'; over time the sense shifted toward 'a distribution of loss' and then to 'a typical amount' or 'mean', from which the modern statistical sense and the abbreviation 'avg' derive.