The median is the middle of the list when the list is sorted.
6,10,11,13,14,14,20,20,23,23,26,27,31,33,38,38
This is the sorted list, so we count evenly up and down the list. In this case, there are 16 total numbers, meaning we count 8 up and 8 down, arriving at 20,23 with the middle being in between them. Both of them can't be the median, so we take the average of these two numbers, which is 21.5. So, the median 21.5.