GMAT Quantitative Section | Question about median

Is it true that when the number of terms in a set is even, then it can’t be concluded that 50% of terms are greater/less than or equal to the median?
But then, the I found the following statement in an official answer: The average of a set of consecutive integers is also the middle of the set, with an equal number of terms greater and smaller than it. 

Is that statement only ALWAYS true for when the number of consecutive terms are NOT even?

---