Do you think if I earn a 3.6-3.8 GPA by the end of junior year of the 4th card marking (if it would count knowing this will be my actual 2nd-semester grade without finals) should I try looking into applying for big average schools like NYU, UMich, UCs, etc. Even though I had a 3.3 GPA avg overall through my past years.
If you have good enough EC's in many areas and are decently profecient in the areas, and your SAT score is top 75%, and you feel like you're confident in your essay writing skills, then yes
My basic back-of-the-envelope math would put your cumulative GPA at a ~3.5 at that point, which is going to be a bit under what schools like NYU, UMich, and the UCs generally look for. You would still have a chance and they might be worth applying to as reaches, but it would likely be small. However, if you have some kind of hook—legacy student, athlete, URM (though the UCs don't care about that), etc.—you would have a better shot. In any case though, I would definitely focus on finding some targets and safeties that would be less competitive and, if it's important to you, less expensive than the schools you mentioned.
I know the most about UMich so I reference that.
You always have a chance but don't count on it as U Mich average acceptance rate is just barely above 25% but for schools like Iowa USC Rutgers and your states flagship all are good options. So have those 3 as your hard target schools but if you're set on them on your application saw something about I slacked fresh and soph year and if you have stellar grades senior year and the other intangibles like rec letters ECs are good you have a shot.
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I wouldn't describe any of those schools as average