Let's call the set of 5 unknown numbers a, b, c, d, and e. We know that the median of this set is 8.
We can consider two cases:
Case 1: The smallest number in the set is less than or equal to 6.
If the smallest number in the set is less than or equal to 6, then adding 2 to it will give us a number less than or equal to 8. In this case, the median of the new set will still be 8.
For example, let's say that a = 4, b = 6, c = 8, d = 10, and e = 12. The median of this set is 8. If we add 2 to the smallest number (a), we get a new set of 5 numbers:
a' = 6, b = 6, c = 8, d = 10, and e = 12.
The median of this set is still 8.
Case 2: The smallest number in the set is greater than 6.
If the smallest number in the set is greater than 6, then adding 2 to it will give us a number greater than 8. In this case, the median of the new set will be greater than 8.
For example, let's say that a = 7, b = 8, c = 9, d = 10, and e = 11. The median of this set is 9. If we add 2 to the smallest number (a), we get a new set of 5 numbers:
a' = 9, b = 8, c = 9, d = 10, and e = 11.
The median of this set is 9, which is greater than 8.
Therefore, an example of a set of numbers for which adding 2 to the smallest number in the set does not change the median is a = 4, b = 6, c = 8, d = 10, and e = 12.