I was recommended to post this question here, instead of on English Language & Usage. In summary, I understand "barely" to mean "equal to, or more than, but not less than" when used with a quantity, but I think this is inconsistent with the definition "certainly not more than" as specified in the Oxford Advanced Learner's Dictionary 7th edition. This is the full definition of "barely" from the Dictionary.
I believe I understand the first and second definition: "barely" implies that something did happen, although it was very close that it didn't. As is also explained here https://english.stackexchange.com/questions/148031/what-does-barely-imply.
However, I am having trouble understanding the third definition, describing a quantity. Using the first example sentence and substituting in the provided words from the third definition, changes how I understand the meaning of the sentence.
To me, stating that
Just 50% of the population voted.
is similar to the definition in 1 and 2 and means the population percentage hit 50%, and maybe trickled over a tiny bit, but it is definitely not less than 50% (don't confuse this usage of just with how it can be used as a synonym for only).
Meanwhile, I interpret
Certainly not more than 50% of the population voted.
as if 50% or less (but probably close to 50%) of the population voted, but definitely not more than 50%.
Combining these two interpretations creates a third definition of "barely", as a synonym to "precisely", meaning no less and no more than 50.000...% of the population voted. I realize this interpretation could also be derived from "just" alone. Maybe this could also be related to the root "bare", as it would be a "naked" 50%, nothing more and nothing less?
Which, if any, of these interpretations is more accurate to how "barely" should be used with a quantity? Does this correct definition reflect the everyday use of "barely", or is it used less strictly to mean "around" or "about" a quantity?