The numbers 12, 16, 19, 23, 28, 30, 35, 37 and \(N\) are arranged in ascending order. The mean of these numbers is equal to their median. What is the value of \(N\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 52
The numbers are already in ascending order, so \(N\) is the largest and the median is the middle (5th) of the 9 numbers. Setting the mean equal to it gives one equation in \(N\).
Median \(=28\)
Sum of the 8 known numbers \(=12+16+19+23+28+30+35+37=200\)
Mean \(\displaystyle=\frac{200+N}{9}=28\)
\(200+N=252\), so \(N=52\)
Check: 52 is larger than 37, so the order stays ascending
The value of \(N\) is 52.
Why the other options are incorrect
Option (1) 70 — Incorrect. With \(N=70\) the mean is 30 but the median is 28.
Option (2) 61 — Incorrect. With \(N=61\) the mean is 29 but the median is 28.
Option (4) 43 — Incorrect. With \(N=43\) the mean is 27 but the median is 28.