Since a real and very precise calendar date of the eruption must have existed, variation in estimations can only be the result of limitations to the carbon-dating method, which, given a plenitude of reliably emplaced samples, can only produce a date within a window of roughly 500 years in a maximum elapsed time of roughly 4000 years or  (12.5%).
Given that a precise calendar date of the eruption must have existed, variations in estimates can only be due to limitations of the carbon-dating technique, which, considering a large number of reliably placed samples, can only provide a date within a range of approximately 500 years at most, over an elapsed time of roughly 4000 years or about 12.5%.