Ans: D
I is true. Note that there are $11$ data. Then the median is the $6$th data. If $m\ge14$, then the $6$th data is $14$.
I is true. Note that there are $11$ data. Then the median is the $6$th data. If $m\ge14$, then the $6$th data is $14$.
II is true. Suppose $m=14$, which is the least possible value. Then we have
$\begin{array}{rcl}
\dfrac{19+10+12+\ldots+14+n}{11} & = & 14 \\
138 + n & = & 154 \\
n & = & 16
\end{array}$
Then, the greatest possible value of $n$ is $16$.
III is true. Consider the mean of the data, we have
$\begin{array}{rcl}
\dfrac{19+10+12+\ldots+14+n}{11} & = & 14 \\
124+m + n & = & 154 \\
m+n & = & 30
\end{array}$
