Suppose, in regards to a class of people, one says that "about 50% of people in this class have a grade of C". Would this statement be incorrect if it turns out that exactly 50% of this class have a grade of C? In other words, does "about" exclude "exactly"?
In other words, does "about" exclude "exactly"?
The way you have framed the question:
Would this statement be incorrect if it turns out that exactly 50% of this class have a grade of C?
about by no means excludes the exact value here.
about means the speaker is making an approximation. Someone generally makes an approximation because the exact value is unknown to them, unimportant to them, or the result involves some calculations which have yet to be made.
If one says
about 50% of people in this class
They mean something like this:
Somewhere between 48% and 52% of the people in this class. I am not sure of the exact number, and/or it's not particularly important right now.
With such an approximation, the speaker is giving a range of possible values. If the figure given in the approximation turns out to be exactly correct, that by no means nullifies the approximation, which refers only to a range of values: It neither commits to, nor excludes, any particular value within that range.
On the contrary: It proves that the approximation was a good one.
ballpark figure and
in the neighborhood are colloquial terms for an approximation - similar to
about, perhaps a bit broader:
"Bill, how much will these renovations cost?"
"I can't say exactly how much."
"OK - give me a
"It will be
in the neighborhoodof $100k."
Consider: If the cost turns out to be exactly $100k, was Bill wrong? Was he lying?
Of course not. Bill gave an excellent approximation - it turned out to be exactly correct.
about adverb (used with a number or quantity) approximately. ‘reduced by about 5 per cent’ - ODO
approximately adverb Used to show that something is almost, but not completely, accurate or exact; roughly. ‘a journey of approximately two hours’ - ODO
Although the definitions appear to say that "about x" excludes "exactly x", the situation is a little more nuanced.
For ease of reference, let's say it was Alice who made the statement in your question that
- about 50% of people in this class have a grade of C
and that Bob checked and found that
- exactly 50% of this class have a grade of C ....
The "not exact" part of the definitions relates to Alice's statement; the exact measurement (Bob's statement) isn't relevant. Note that the claim isn't that the figure Alice quotes (50%) is inaccurate, but that there is some wiggle room in that figure. In other words, Alice isn't making an exact or accurate claim, but that's quite a different thing from saying that Alice is claiming the figure of 50% is inaccurate or inexact.
So if Bob finds that the number Alice quoted was actually exactly correct, that doesn't invalidate Alice's claim.
In answer to your question, then, "about" does include "exactly" in the sense used above.
About, around, circa, rougly all suggest rounding off a percentage to a readily understood fraction that will convey more meaning: if I say about half my rosebushes have spider mites, it has more impact than saying 45.276%. Anyone to whom I told the unwieldy figure would simply round up anyway: “Hmm… that's about half.”
If an instructor determines that exactly 50% of the class earned a C, then there would be no reason to withhold that information. That assumes that there are an even number of students and exactly half got a C.
If, say, the class has 33 students and 15 of them got a C, then 45.454546% got a C, which one could round up to about 50% or "half."
So to answer your question, no, approximate and exact are mutually exclusive concepts.