9. Let the set $M=\{1,2,3, \cdots, 2002\}$, and for any non-empty subset $A$ of $M$, let $x_{A}$ be the sum of the largest and smallest numbers in $A$. Then the arithmetic mean of all such $x_{A}$ is $\qquad$
9. 2003.

Pair the non-empty subsets of $M$. For a non-empty subset $A \subset M$, let $A^{\prime}=\{2003-a \mid a \in A\}$. Then, when $A^{\prime} = A$, $x_{A}=2003$; when $A^{\prime} \neq A$, $x_{A}+x_{A^{\prime}}=2003 \times 2=4006$. Therefore, the arithmetic mean sought is 2003.