is the mean always to a value in the data set

Question

number sense

Answer 1

I assume you meant to ask "Is the mean always EQUAL to a value in the data set?"  The answer is NO.  It could be, but it does not have to be.  Example:

 

Data set {4,5,7}

 

Mean = (4 + 5 + 7)/3 = 16/3 ≅ 5.33,

 

which is not in the data set.  An example where the mean is in the data set is {1,2,3}.

 

Mean = (1 + 2 + 3)/3 = 6/3 = 2, which in this case is in the data set.