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)

$1$

Mean of $(7,8,9,7,8,7,\lambda ,8)=8$

$\frac{7+8+9+7+8+7+\lambda +8}{8}=8$

Solving we get $\lambda =10$

Now, variance

$=\frac{\sum (x-\overline{x}{)}^2}{N}$

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

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

$=\frac{8}{8}$

$=1$.