The numbers 9, 13, 15, 20, 22, 24, 26, 29 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 1
The correct answer is Option (1) → 40
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 \(=\) 5th number \(=22\)
Sum of the eight known numbers \(=9+13+15+20+22+24+26+29=158\)
Mean \(\displaystyle=\frac{158+N}{9}=22\)
\(158+N=198\), so \(N=40\)
Check: 40 is larger than 29, so the order stays ascending
The value of \(N\) is 40.