Question 2
A finite set $\mathcal{S}$ of distinct real numbers has the following properties: the mean of $\mathcal{S} \cup \{1\}$ is $13$ less than the mean of $\mathcal{S},$ and the mean of $\mathcal{S} \cup \{2001\}$ is $27$ more than the mean of $\mathcal{S}.$ Find the mean of $\mathcal{S}.$