13. From the set $\{1,2, \cdots, 11\}$, two elements are selected to form a new set. There are ( ) new sets whose elements have an average value of 6.
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
13. D.

Notice,
$$
\frac{1+11}{2}=\frac{2+10}{2}=\frac{3+9}{2}=\frac{4+8}{2}=\frac{5+7}{2}=6 \text {. }
$$

Therefore, the sets of two elements that satisfy the condition are $\{1,11\} 、\{2,10\} 、\{3,9\} 、\{4,8\} 、\{5,7\}$, totaling 5 kinds.