Q. The mean of the numbers $a,b,8,5,10$ is 6 and the variance is 6.80. Then, which one of the following gives possible values of $a$ and$b$?
A) $a = 3,\ b = 4$
B) $a = 0,\ b = 7$
C) $a = 5,\ b = 2$
D) $a = 1,\ b = 6$
Explanation
(a)
According to the given condition
$6.80 = \frac{\left\lbrack \begin{array}{r}
(6 - a)^{2} + (6 - b)^{2} + (6 - 8)^{2} \\
+ (6 - 5)^{2} + (6 - 10)^{2}
\end{array} \right\rbrack}{5}$
$\Rightarrow 34 = (6 - a)^{2} + (6 - b)^{2} + 4 + 1 + 16$
$\Rightarrow (6 - a)^{2} + (6 - b)^{2} = 13 = 9 + 4 = 3^{2} + 2^{2}$
$\Rightarrow \ \ \ a = 3,\ b = 4$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.