Nine different numbers have a median of 31.6. Each of the four smallest of these numbers is reduced by 3. What is the median of the nine numbers after this change?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 31.6
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: \(a_1<a_2<\dots<a_9\), with \(a_5=31.6\)
The four smallest numbers are \(a_1, a_2, a_3, a_4\), all below 31.6
Reducing each of them by 3 makes them still smaller, so they stay below \(a_5\)
\(a_5, a_6, \dots, a_9\) do not change, so \(a_5\) is still the 5th number in order
The median stays 31.6; only the mean falls.