Nine different positive numbers have a median of 62.4. Each of the four largest of these numbers is doubled. What is the median of the nine numbers after this change?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 62.4
For 9 numbers written in ascending order, the median is the 5th 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 5th number is 62.4
The numbers that change are the four largest numbers, all on one side of the middle
After the change they become still larger (each is positive, so doubling makes it bigger), so they stay on the same side of the 5th number
The middle number itself does not change, so it is still the 5th number in order
The median stays 62.4; only the mean changes.
Why the other options are incorrect
Option (1) 124.8 — Incorrect. This doubles the median, but the median (the 5th number) is not one of the four numbers that are doubled.
Option (2) 93.6 — Incorrect. This takes the median halfway between 62.4 and its double; the median does not move at all.
Option (3) 31.2 — Incorrect. This halves the median; the changed numbers grow, and the middle one stays.