The storing method is according to the ripeness of the avocado:
Ripe Avocados
Room temperature (it will be over-ripe in 1-2 days),
Refrigerator (can be stored for 2-3 days)
Half-ripe Avocados
Room temperature (ripe in 1-2 days),
Refrigerator (can be  stored for 4-6 days)
Unripe Avocados
Room temperature (2-3 days to ripe),
Refrigerator (can be stored for 7-14 days)