The numbers 3, 10, 13, 17, 22, 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 2
The correct answer is Option (2) → 36
The numbers are already in ascending order, so \(N\) is the largest and the median is the average of the 4th and 5th numbers. Setting the mean equal to it gives one equation in \(N\).
Median \(=19.5\)
Sum of the 7 known numbers \(=3+10+13+17+22+26+29=120\)
Mean \(\displaystyle=\frac{120+N}{8}=19.5\)
\(120+N=156\), so \(N=36\)
Check: 36 is larger than 29, so the order stays ascending
The value of \(N\) is 36.
Why the other options are incorrect
Option (1) 60 — Incorrect. With \(N=60\) the mean is 22.5 but the median is 19.5.
Option (3) 44 — Incorrect. With \(N=44\) the mean is 20.5 but the median is 19.5.
Option (4) 52 — Incorrect. With \(N=52\) the mean is 21.5 but the median is 19.5.