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Default averaging a column of letter grades into a numeric GPA

In my spreadsheet, column A contains letter grades (A, A-, B+, etc.). I have
a GPA reference table in F1:G11, with F1="A", G1=4; F2="A-", G2=3.67; and so
forth.

Now, I know how to use VLOOKUP to turn an individual letter grade into a GPA
value. In B2, I have the formula =VLOOKUP(A2,$F$1:$G$11,2,FALSE), and that
works fine.

What I want to do is to find the average GPA value of all the letter grades
in column A. That's easy if I create a new column of data, column B,
containing copies of the formula given above. But I don't want that
intermediate step. How can I get the average GPA value without creating a
new column of data?

Many thanks.
 
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