AHSME 1968 Problem 17

Let $f(n)=\frac{x_1+x_2+\cdots +x_n}{n}$, where $n$ is a positive integer. If $x_k=(-1)^k, k=1,2,\cdots ,n$, the set of possible values of $f(n)$ is: $\text{(A) } \{0\} \text{(B) } \{\frac{1}{n}\} \text{(C) } \{0,-\frac{1}{n}\} \text{(D) } \{0,\frac{1}{n}\} \text{(E) } \{1,\frac{1}{n}\}$