AHSME 1962 Problem 8

Given the set of $n$ numbers; $n > 1$, of which one is $1 - \frac {1}{n}$ and all the others are $1$. The arithmetic mean of the $n$ numbers is: $\textbf{(A)}\ 1 \textbf{(B)}\ n-\frac{1}{n} \textbf{(C)}\ n-\frac{1}{n^2} \textbf{(D)}\ 1-\frac{1}{n^2} \textbf{(E)}\ 1-\frac{1}{n}-\frac{1}{n^2}$