In arithmetic statistics, we study properties of arithmetic objects as they vary over a family. In this lecture, we will give an overview of some of the methods used in arithmetic statistics, focusing on the question of studying ranks of elliptic curves. Conjectures of Goldfeld and Katz-Sarnak state that the average rank of elliptic curves is 1/2. I will describe joint work with Bhargava where we show that the average rank is finite, and in fact less than 1.