A list consists of five distinct positive real numbers. One number is removed, leaving a list of four numbers.
Consider the statements
- : The number removed equals the mean of the original list.
- : Both the mean and the median are unchanged by the removal.
Which of the following is correct?
A is sufficient but not necessary for .
B is both necessary and sufficient for .
C is necessary but not sufficient for .
D is neither necessary nor sufficient for .