For a set of 11 distinct observations arranged in order, the median is the 6th observation (with 5 observations before it and 5 after it).
The original set in order:
Position: 1st, 2nd, 3rd, 4th, 5th, 6th, 7th, 8th, 9th, 10th, 11th
The 6th observation =22.5 (the median)
The largest 5 observations are at positions 7th, 8th, 9th, 10th, and 11th.
When each of these 5 observations is increased by 5, the observations at positions 1st through 6th remain unchanged.
After the modification:
Positions 1-6: unchanged
Positions 7-11: each increased by 5
The median is still the 6th observation, which remains 22.5.
The median of the new set =22.5
The median remains the same as the original set because only observations after the median position were modified, leaving the 6th position unchanged.
Therefore, the correct answer is option 3: remains the same as that of the original set.