"Amount of boxes" vs "number of boxes" in non discrete graph

The distinction made in English is slightly different to the one made in mathematics. Here the distinction is between countable and uncountable nouns.

For countable nouns (such as person, dog, pen and box):

• a/an are used to refer to one (indefinite) item
• Number is used to describe how many

For uncountable nouns (such as sugar, paint and so on):

• some is used to refer to an (indefinite) quantity
• amount (or another word, such as quantity) is used to describe how much

Note that this is a property of the nouns, rather than the substances involved - so I would say some paint, but a gallon of paint, since gallon is countable (even though I'm still talking about paint).

In this example, since you are talking about boxes, which are countable, it sounds better to use number - even though the number in question might not be a whole number.

Even though you're not giving an integral number of boxes, so you should use number of boxes per minute, because the correct term for measuring boxes is number and not amount.

It sounds something like a question about continuous versus discrete variables, but "discrete" does not mean "integer". I am not sure there is a special word for a graph that shows non-integral values...it's not like you are "smoothing" the graph, right?