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I think you're confusing this due to the common incorrect use of "that" in relation to data as if it's something singular, id est, "Could you please provide me that data?"
Technically this is grammatically incorrect (and yes before you ask, I say "those data"), but I've come to understand that people actually mean "data set" when they say this, and are just omitting that word from the sentence.
Since that is all that's needed to have everything correctly agree again, I can just fix it in my head when I hear it so that my brain doesn't explode.
I really dont think I am. I really do think it's a mass noun.
I'm not sure why you think that. By definition (which you even gave in your original post) that would mean that data are something that can't be broken down into individual, countable units.
But there is a smallest unit, which is called a bit. Data can be broken down into smaller, countable units. So the word doesn't fit the common definition of what a mass noun is.
That's not a particularly compelling argument. There's a smallest unit of sand, too, but we still use a mass noun for it.
Besides, dictionary researchers agree it's both a mass noun and a plural noun. People use it both ways. Here's what Merriam Webster says about it. (I'm going to rework it to reduce the wordiness because it was so dense!)
So OP's post is only half right, if even that much. In common speech, data is a mass noun, but many scientists and publishers still treat it as a plural noun. I would even venture most do.
Working as a programmer, most people I've interacted with use it as a mass noun, but not all. Language evolves, and the mass noun version is just as acceptable in most circles, but it certainly isn't worthy of a "you should know" or "today I learned it's actually a mass noun."