differences - "An" average of vs. "The" average of


When nouns such as average, total, sum, etc., are modified by a prepositional phrase, how do you choose between the definite and indefinite articles? I cited sentences 1, 3, and 5 below from various sources on the Internet. As an English learner, I have always wondered what difference there is if the indefinite article is replaced by the definite article. Are sentences 2, 4, and 6 below correct or possible?


Here are example sentences:



  1. He finished the season with a batting average of .357.


  2. He finished the season with the batting average of .357.




  3. That will use a total of about 3.3 million tons of lead.




  4. That will use the total of about 3.3 million tons of lead.




  5. What two prime numbers have a sum of 7?



  6. What two prime numbers have the sum of 7?


I would appreciate your help much.



Answer



You have an (or a) average, maximum, minimum, or other group-based calculation of something, while you take (or calculate) the average, maximum, or minimum.


Thus your samples 1, 3, and 5 are correct, but not 2, 4, or 6.


(To clarify, as per the comments: In the example sentences, the average is a property that is already known, and it is being treated grammatically in the same way as a generic, indefinite possession and thus can take the indefinite article 'a'. If the average is an unknown number that needs to be determined, then you are taking or calculating it, and then it is a specific feature and should be referred to with the definite article 'the'.)


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