Question

If the mean of the data of observations 12, 7, 9, 5, 15, 10, 9, 8, 6, 4, 2, x, y, z is 8, where x, y, z are natural numbers and 5 < z < x < y < 12, then which of the following cannot be the value of x, y, z respectively?

• A. x=9, y=10, z=6
• B. x=8, y=10, z=7
• C. x=8, y=11, z=6
• D. x=9, y=11, z=5

Answer 1

The correct option is D x=9, y=11, z=5

Given that x, y, z are natural numbers and mean of the observations is 8.
Mean = $\frac{Sumofobservations}{Numberofobservations}$
$\Rightarrow \frac{12+7+9+5+15+10+9+8+6+4+2+x+y+z}{14}=8$
$\Rightarrow 87+x+y+z=112$
$\Rightarrow x+y+z=25$
Also, it is given that 5 < z < x < y < 12.
However, in option (4), the value of z = 5 which is not possible as z > 5.
Hence, the correct answer is option d.