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Parrot???? I asume that you are referring to a Venus Tusk Fish. Most refer to them as parrot but infact they don't have a parrot like beak like the parrot fish does. (sure look like a parrot though) The biggest Parrot fish is the bulbermattapon (latin name, not sure about the spelling) and it grows to about 1.2m in length.
A venus tusk fish on the other hand, as its name implies has tusks and no beak, the biggest tusky,bluey that I have seen was 12.95kg and the biggest reported one was 13.1kg both caught in Moreton Bay. Don't ask me the average size though but around the 2 to 5kg mark would be about the average size of most fish caught.