Seven different numbers have a median of 24. Each of the three smallest of these numbers is decreased by 7. What is the median of the seven numbers after this change?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 24
For 7 numbers written in ascending order, the median is the 4th 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 4th number is 24
The numbers that change are the three smallest numbers, all on one side of the middle
After the change they become still smaller, so they stay on the same side of the 4th number
The middle number itself does not change, so it is still the 4th number in order
The median stays 24; only the mean changes.
Why the other options are incorrect
Option (2) 21 — Incorrect. This takes away the fall in the mean, \(3\times7\div7=3\), from the median; the median itself does not move.
Option (3) 17 — Incorrect. This subtracts 7 from the median, but the median (the 4th number) is not one of the three numbers that change.
Option (4) 31 — Incorrect. This adds 7 to the median; the three smallest numbers fall, and the middle one stays.