Can a median value occur twice?

Question

From a practice exam:

From the set $$\{7, 12, 5, 16, 23, 44, 18, 9, Z\},$$ which of the following values $Z$ be equal to if it is the median of the set?

Choose from: $14, 11, 12, 17, 21.$

$14$ was given as the correct answer.

But, arranging the numbers in increasing order with $Z = 12$ gives $$5, 7, 9, 12, 12, 16, 18, 23, 44,$$ in which case the median is $12,$ no?

Answer 1

The wording would have been "from the list" then $12$ would be possible, but "set" appears explicitly so elements have to be considered unique (set with repeated elements are called multisets).

Note also that when a set has an even number of elements, then we generally consider that the median is the average of the two central elements.

So would $Z=12$ then the set would in fact be $\{5,7,9,12,16,18,23,44\}$ and the median would actually be $(12+16)/2=14$ not $Z$.