Question

If the mean of the data : $7, 8, 9, 7, 8, 7, \lambda , 8$ is $8$, then the variance of this data is :

• A. $\frac{7}{8}$
• B. 1
• C. $\frac{9}{8}$
• D. 2

Answer 1

Answer: (B)

Given :-
Mean $(\bar{x})=8=\frac{7+8+9+7+8+7+\lambda+8}{8} $
$\Rightarrow 64=54+\lambda$
$ \Rightarrow \lambda=10 $
Therefore variance $\left(\sigma^{2}\right)= \frac{\Sigma\left(x_{i}-\bar{x}\right)^{2}}{8} $
$=\frac{1}{8}\left((7-8)^{2}+(8-8)^{2}+(9-8)^{2}+(9-8)^{2}+(7-8)^{2}+(8-8)^{2}+(7-8)^{2}+(10-8)^{2}+(8-8)^{2}\right.$
$=\frac{1}{8}(8)=1$