As far as the inscription is concerned, remember that this is an abbreviation of a transcription. There are various ways of expressing an age on a gravestone.
You need to look at the original to see whether is says, 'aged xx years' or 'in the xxth year of his/her age'.
If it says, 'aged xx years' I would take that to mean that the deceased person's last birthday was their xxth.
If it says, 'in the xxth year of his/her age', I would take that to mean that the person's next birthday would have been their xxth.
But of course this has nothing to do with the *accuracy* of the quoted age, which is often wrong on both gravestones and in records like the census.