'average' originates from Old French 'avarie' (also Medieval Latin 'avaria'), ultimately from Arabic 'ʿawār' meaning 'defect, damage'; in late medieval use it referred to shared cost or loss (especially in shipping).

'average' changed from Old French 'avarie' (meaning 'damage, loss') and Medieval Latin 'avaria' (a loss to be divided) to Middle English usages about shipping losses and then to later meanings treating a common share or typical amount; the verb sense 'to compute the average' developed from these financial/distributive senses.

Initially, it meant 'loss or damage (to be shared among owners)', but over time it evolved into senses related to a common share and then into the statistical sense of a 'typical or mean value' used in modern English.