<p>The lower scores belong to students who are in need at or dearly wanted by the college (athletes, legacies) or who have a very good reason (had to overcome terrible odds even to make it to that score). International students must be at least at the median but typically would need to be into the top 25%. For Yale, you should aim for 2100 at the very least. Every single element can get you rejected but that’s not sufficient, you also need to have a compelling combination of factors AND be better than everyone else. Essentially, you need to be the best academically from your country and the most compelling, too.
You should absolutely apply, but start reading The Fiske Guide, or Insider’s Guide to the Colleges, or The Princeton Review’s Best Colleges and build a good list with half colleges that seem “easy to get into” to you - I can guarantee that they will turn out to be harder to get into than you thought, especially if you have a lot of financial need. Some colleges can only fully fund 3 or 4 international students… out of hundreds who apply.</p>