The numbers of something or the number of something

Solution 1:

Well, "the number" alone is strictly singular in itself. And when "of" is added, the phrase, "the number of", will call for a plural noun (i.e. trees)

Personally, I have never seen the statement "the numbers of..." when describing or assessing a graph or a data set. Commonly, you use "the number of" because you are specifically describing or referring to a one particular thing in the graph as in:

"the number of students who wish to study abroad next year"

Likewise for rate.

"the rate of change in the annual global temperature"

Why would "number" and "rate" be plural anyways when you will be referring to one concept or set of things observable from a graph?