How does average profile of person that got accepted into top university look like?
How does average profile of person that got accepted into top university look like? 


For reasons mentioned in the comments, I will just briefly address grad school: It's typical to have taken a number of advanced classes (possibly including graduate classes) in your discipline from a good school, and to have done well in them.  You should have strong letters of recommendation.  In some fields (not in math, and I don't think in CS) it's typical to have done some research.  It's pretty common to be international, and straight out of another (bachelors or master's) program.  But I don't know that an "average profile" is the right thing to look at.


  What does one need to have to feel reasonably secure about being accepted into top universities?


You're not in a good position to judge yourself, so talk to your professors.  What kind of schools do they think you should apply to?  What kinds of schools do they think you can get into?  After all, they'll be writing letters for you, which are one of the primary factors in deciding your admissions.