Let ${\rm Kl}(a,b;n)$ be the usual Kloosterman sum modulo $n$, with coefficients $a$ and $b$. We give upper and lower bounds for the sum $ \sum_{n\leq x} \vert {\rm Kl} (1,1;n)\vert /\sqrt n, $ and for related sums, by using large sieve techniques and Deligne-Katz theory of exponential sums. Extensions to more general exponential sums of dimension one are also given.