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?

then `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 `ballpark figure`".

"It will be `in the neighborhood` of \$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.

• I'm not advocating either side, but did you see the definition in my post? Every definition of approximation I've seen emphasises "not exact", that's the sense in which I agree with KarlG, the definition of approximation in each definition excludes exactness. – Zebrafish Mar 25 '18 at 6:16
• @Zebrafish - No, it is not exact. It is only an approximation. But an approximation does not exclude any particular value within a reasonable range. Any value within the range of the approximation is included. I set the range at 2% +/- , but that's a somewhat arbitrary range. When we round off numbers, according to common rounding convention anything <5 goes to closest value below, >= 5 to closest value above, for example: \$40.45 is rounded to \$40; \$40.55 is rounded to \$41. Even when exact value is known we can use an approximation and remain accurate, in terms of our approximation. – Vector Mar 25 '18 at 6:33
• That's all good, but you didn't address the fact that the definition of "approximation" in all dictionaries I've seen is "but not exact." Also, we're not necessarily talking about rounding here, some things are approximated as integers and not rounded. For example, "There are about 6 boys in the room." And it turns out there are exactly six, it fails the description of approximation, because it is exact. There is no rounding to speak of. – Zebrafish Mar 25 '18 at 6:45
• @Zebrafish but you didn't address the fact that the definition of "approximation... . I did: But an approximation does not exclude any particular value within a reasonable range You are not understanding that definition correctly. – Vector Mar 25 '18 at 6:47
• "That it happens to be very accurate does not negate the fact it is an approximation." It's more than "very accurate" it's exact. – Zebrafish Mar 25 '18 at 7:03

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.

• Fine answer. This is exceedingly simple - not sure why some are having such great difficulty with it. – Vector Mar 25 '18 at 20:03

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.

• Say the instructor didn't withhold the information, but made an estimate and that estimate turned out to be exact, is the statement still wrong? – Zebrafish Mar 25 '18 at 4:56
• @Zebrafish: It means the statement is no longer strictly accurate and would likely be revised. – KarlG Mar 25 '18 at 4:59
• @Vector Does the same go for the other answer? – Zebrafish Mar 25 '18 at 5:06
• @KarlG : would likely be revised - Not so. Approximations are often used simply because there is no need for the precision of an exact value and/or it may be impossible ever to determine the exact value. Rounded numbers are approximations - they are used constantly in business. They are never revised. Business people frequently don't care about the pennies or sometimes even hundreds or thousands of dollars: They are interested only in gross approximations - they are sufficient for their purposes. – Vector Mar 25 '18 at 6:39
• @Zebrafish - Richard Haven's answer is unclear. My understanding is that "No" is in answer to the question "does "about" exclude "exactly"? : The answer is No, it does not. Perhaps I don't understand that answer correctly. – Vector Mar 25 '18 at 6:43