What positive integer must be included in the set(1, 2 , 4 , 8) so that the new set of five integers have a median that is equal to its mean

Steps on how to get 5:
1. If you added 5 to the list of numbers, the median would be 4.
1,2,4,5,8
Since 4 is directly in the middle.
2. Now you find the mean
1 + 2 + 4=7
5 + 8= 13
13 + 7= 20
3. Now divide 20 by 5
4. Your mean is 4
5. By adding 5 to this list of numbers, you get the same mean and median which is 4

What are the options?