Eleven different numbers have a median of 47.5. Each of the five largest of these numbers is increased by 11. What is the median of the eleven numbers after this change?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 47.5
For 11 numbers written in ascending order, the median is the 6th number. It depends only on which value stands in the middle, not on how far the other values are from it.
Write the numbers in ascending order; the 6th number is 47.5
The numbers that change are the five largest numbers, all on one side of the middle
After the change they become still larger, so they stay on the same side of the 6th number
The middle number itself does not change, so it is still the 6th number in order
The median stays 47.5; only the mean changes.
Why the other options are incorrect
Option (1) 58.5 — Incorrect. This adds 11 to the median, but the median (the 6th number) is not one of the five numbers that change.
Option (3) 36.5 — Incorrect. This subtracts 11 from the median; the changed numbers are above the middle and grow larger.
Option (4) 52.5 — Incorrect. This adds the rise in the mean, \(5\times11\div11=5\), to the median; the median itself does not move.