Mostly I'm wondering what kind/what tier of programs I should be aiming for since I'll be applying this fall (current senior). Obviously my GPA and lack of research will keep me out of Stanford and the like, but I'm hoping that I have a shot elsewhere. Also any tips to help my application would be greatly appreciated.
Undergrad college: top 10 LAC according to US news
Major: Math
GPA: 3.1 (ouch) with an upward trend
Math courses: the standard fare
Stats courses: Probability
GRE: 161V, 167Q, 4.0AW
Research experience: none
I'm planning on taking more stats courses this year but as it stands, my letters of recommendation will be written by pure math professors. I'm also considering taking a year off so that I can apply with more stats courses under my belt but I don't know how useful that would be since most of the programs I've seen only require students to have gone through the Calc sequence + Linear algebra.
Also I should mention that I would be completely open to obtaining an MS first in order increase my GPA, but I'm not aware of which programs provide funding for masters.
Am I reasonable to apply to schools like Northwestern, NYU, BU, Virginia Tech, etc.?