I think there are several different points here that should be taken into account. I must state that the following is all anecdotal and based on my own observations.
First, there is the question of use/register. In e.g, statistics, science, and academic papers in general, data is a (countable) plural word, whereas in day-to-day spoken English, in the UK at least, it is usually taken as a singular (mass) noun and requires a singular verb. In the latter case, amount would be perfect as it is also (and grammatically) a mass word.
Second, there is a trend in US English for mass nouns to be converted into countables and, as in the case of so much other American English, this trend is spreading to other English-speaking countries, and especially to the younger generations therein. So, whether you use amount or number can very much depend on the context.
That said, how about some alternatives? I would suggest quantity can be used for both countables and uncountables and volume of data could also be used/preferable (especially when talking about Big Data, for example).