Averaging your two GPAs from the two different universities will only be accurate if you have taken the exact same number of courses, with the same weightings, at each university. Since you're getting a different GPA when you calculate the overall average using each individual course, I can only assume you took more courses at one university than at the other. In that case, the cumulative GPA averages are not equally weighted - one average takes more courses into account, and thus should be weighted more heavily. If you took, say, 8 courses at your first uni and 6 at your second (for a total of 14 courses), in your calculation you have to take that into account, so the average calculation would look like this:
(8(3.16)+6(2.70))/14= 2.96
(This is just an example, obviously, since I don't actually know how many courses you took at each institution. You'd have to replace the 8 and 6 with whatever number of courses you took at each one.)
I didn't apply through Optomcas, so I'm not sure how it calculates GPA, but I would assume it just figures it out by averaging the grade you got in each individual course, regardless of what school it was at.
Your error in your third calculation is that you're once again weighting each GPA wrong. By averaging your overall (false) cGPA from the two universities and the GPA from each summer course, it's like you're saying that those two summer courses together are worth the equivalent of however many courses you took at both universities. In other words, if you took 8 courses at Uni 1 and 6 courses at Uni 2, for a total of 14 courses, that cGPA takes 14 course grades into account. By averaging the cGPA with the 3.7's and dividing by three, it's like saying that those two 3.7's were each worth the equivalent of 7 courses, so they are incorrectly giving your GPA a huge boost. The more values you include in an average calculation, the less each value actually changes the overall average.
Does all that make sense? Essentially what you need to do is average all your grades, from both institutions, and divide by the total number of courses, or units or whatever, that you've taken (let's call it n). Seems like you've done that, and it gave you a 3.0, which is what your true cGPA is. To figure out what it would be after getting a projected 3.7 in each summer course, you would need to add two 3.7's to your original calculation that included all the course grades, and then divide by the total number of courses you would have taken by that point (so n+2). That cGPA will likely not be 3.44, I'm afraid, because the two summer courses aren't going to change it that much - if you did get a 3.7 in both of them, they would boost your GPA, but probably not by a lot unless you haven't taken very many classes to begin with.
ok...
so i attended two different universities and i know how optomcas calculates gpa..the problem is.
at institution 1 cumulative gpa is:3.16
at institution 2 cumulative gpa is: 2.7
so this is how i did it. (3.16+2.7)/2 =2.93
and this spring i will also be taking 2 more classes assuming i get: 3.7 and 3.7 in both classes so..
(2.93+3.7+3.7)/3= 3.44
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but i am unsure if this is how they will do it.. because every time i calculate the average using each individual class i get a different gpa (3.0).. but when i use the cumulative gpa's and average them out, i get a different gpa?
does anyone know what im doing wrong?
this is very confusing because i thought that by the time i applied i would have a 3.4...