If the mean of the numbers \(2, (2p+2), 7, 13, 17, 4\) and \((p-1)\) is 8, then find their median.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7
The mean fixes \(p\); the median is then the middle value once the seven numbers are arranged in order.
Sum of the numbers \(=2+(2p+2)+7+13+17+4+(p-1)=3p+44\)
Mean 8 for 7 numbers, so the sum is \(7\times8=56\)
\(3p+44=56\), so \(p=4\)
The numbers: 2, 10, 7, 13, 17, 4, 3
In order: 2, 3, 4, 7, 10, 13, 17; the 4th of the seven is the median, 7