I need to solve this problem for an arbitrary N. I'm not exactly sure how to go about this. I have formulas to calculate both standard deviation and MAD, however I'm not sure what to do with the hint at the bottom. I believe it will help me calculate the sample variance which will give me the standard deviation (the square root of the sample variance), but I'm not sure. Can someone point me in the right direction?
You're thinking in the right direction. Work from first principles (i.e., the very definition of variance).