Question

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

Answer 1

$\Rightarrow$ Given numbers are $7,8,9,7,8,7,\lambda ,8$

$\Rightarrow$ $\overline{x}=8$

$\therefore$ $\overline{x}=\frac{7+8+9+7+8+7+\lambda +8}{8}$

$\therefore$ $8=\frac{54+\lambda }{8}$

$\therefore$ $\lambda =10$

$Variance=\frac{(7-8{)}^2+(8-8{)}^2+(9-8{)}^2+(7-8{)}^2+(8-8{)}^2+(7-8{)}^2+(10-8{)}^2+(8-8{)}^2}{8}$

$=\frac{1+0+1+1+0+1+4}{8}$

$=\frac{8}{8}$

$=1$

$\therefore$ $Variance=1$