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}.
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}.