If mean of the numbers 2, (p+1), 8, 19, 16, 3 and p is 9, then find the mode of the numbers.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
The mean is the sum divided by the number of values; it gives \(p\). The mode is the value that occurs most often.
Sum: \(2+(p+1)+8+19+16+3+p=2p+49\)
Mean of the 7 numbers: \(\displaystyle\frac{2p+49}{7}=9\), so \(2p+49=63\) and \(p=7\)
The numbers are 2, 8, 8, 19, 16, 3, 7
8 occurs twice and every other number once, so the mode is 8