Let N(L,t) be the number of points of a lattice L inside a ball of radius t centered at the origin in R^n. It is easy to see that N(L,t) grows proportionally to the volume of the ball for large t, but how much does the actual count deviate from this volume? Hardy conjectured a lower bound for the integer lattice L=Z^2 in R^2 being proportional to the square root of the volume of the ball, based on a simple heuristic. If we regard the lattice L as a random variable chosen from some small neighborhood of a fixed lattice, we may ask for a bound on the standard deviation of N(L,t). I will talk about how one may prove that this standard deviation of N satisfies a lower bound proportional to the square root of the volume of the ball of radius t.