M is the data set 50,81,75,63,65,48,72,X, where X is an integer. The mean of M is an
integer, and is greater than or equal to the smallest data value of M and less than or equal to
the largest data value of M, neither of which is X. List all possible values of X that would
cause set M to have a unique mode.

Question

M is the data set 50,81,75,63,65,48,72,X, where X is an integer.  The mean of M is an 
integer, and is greater than or equal to the smallest data value of M and less than or equal to 
the largest data value of M, neither of which is X.  List all possible values of X that would 
cause set M to have a unique mode.

phi · Answer

The mode is the number repeated most often.  It sounds like X is not 50 or 72.  So to get a different mode, X must match one of the remaining numbers.