How does grad school view a consistent B average in a course sequence? I'm a math major, and in an undergraduate real analysis sequence I got a B- and B over the two semesters. A year later I took the first year graduate real analysis sequence and got a B+ and a B over the two semesters. I know there's a lot of outside factors to consider, but in general how do these grades affect my ability to get a Master's in Statistics and a PhD in Computer Science?

My overall GPA is an A-. How can I remedy this track record if it looks negative? Does it involve taking even higher level courses in Real Analysis  (i.e., comparable to 6000 level) and getting A's?
Although this might be a showstopper for some specific schools), this need not be a show stopper in general. Especially if you have at least one very strong letter of recommendation.  My answer is based on the assumption that you would apply for CS or statistics, which are just tangential enough to be able to pass muster from most people's point of view.

It could be more harmful if the B sequence were exactly aligned with what you're going to apply for.  But it isn't.

(There are of course other ways to increase your chances, e.g.: don't apply late; if there's a subject GRE required, a strong score here could help; get some feedback on your essay draft.)