Let $R$  be a set of nine distinct integers. Six of the elements are $2$, $3$, $4$, $6$, $9$, and $14$. What is the number of possible values of the median of $R$?
$\textbf{(A)}\hspace{.05in}4\qquad\textbf{(B)}\hspace{.05in}5\qquad\textbf{(C)}\hspace{.05in}6\qquad\textbf{(D)}\hspace{.05in}7\qquad\textbf{(E)}\hspace{.05in}8$
First, we find that the minimum value of the median of $R$ will be $3$. 
We then experiment with sequences of numbers to determine other possible medians.
Median: $3$
Sequence: $-2, -1, 0, 2, 3, 4, 6, 9, 14$
Median: $4$
Sequence: $-1, 0, 2, 3, 4, 6, 9, 10, 14$
Median: $5$
Sequence: $0, 2, 3, 4, 5, 6, 9, 10, 14$
Median: $6$
Sequence: $0, 2, 3, 4, 6, 9, 10, 14, 15$
Median: $7$
Sequence: $2, 3, 4, 6, 7, 8, 9, 10, 14$
Median: $8$
Sequence: $2, 3, 4, 6, 8, 9, 10, 14, 15$
Median: $9$
Sequence: $2, 3, 4, 6, 9, 14, 15, 16, 17$
Any number greater than $9$ also cannot be a median of set $R$. 
Therefore, the answer is $7\implies \textbf{(D)}.$