7. Let $S=\{1,2, \cdots, 11\}$, for each seven-element subset of $S$, arrange the seven numbers in ascending order, and take the middle number. Then the sum of all the middle numbers taken is $\qquad$
7. 1980.
The number of 7-element subsets of $S$ is $\mathrm{C}_{11}^{7}$.
For each 7-element subset
$$
A=\left\{a_{1}, a_{2}, \cdots, a_{7}\right\}\left(1 \leqslant a_{1}12-a_{2}>\cdots>12-a_{11} \geqslant 1\right).
$$
The middle numbers of sets $A$ and $B$ are $a_{4}$ and $12-a_{4}$, respectively, and their sum is 12.
Therefore, the sum of all middle numbers is
$$
\frac{C_{11}^{7}}{2} \times 12=1980 .
$$