The median of a set of 11 distinct observations is 22.5. If each of the largest 5 observations of the set is increased by 5, then the median of the new set
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → remains the same as that of the original set.
The median of 11 values arranged in order is the 6th value, with 5 values below it and 5 above it. It depends only on which value is in the middle, not on how large the other values are.
The 5 largest values are the 7th to the 11th, all above the median
Adding 5 to each makes them larger still, so they stay above the 6th value and the order does not change
The 6th value is still 22.5, so the median does not change