Question

If mean and standard deviation of $5$ observations $x_1,x_2,x_3,x_4,x_5$ are $10$ and $3$, respectively, then the variance of $6$ observations $x_1,x_2,....,x_5$ and $-50$ is equal to :

• A. $582.5$
• B. $507.5$
• C. $586.5$
• D. $509.5$

Answer 1

Answer: (B)

$507.5$

$\overrightarrow{x}=10\Rightarrow {\sum }_{i=1}^5{x}_i=50$
$S.D.=\sqrt{\frac{{\sum }_{i=5}^5{x}_i^2}{5}-(\overline{x}{)}^2}=8$
$\Rightarrow {\sum }_{i=1}^5(x_i{)}^2=109$
Variance $=\frac{{\sum }_{i=1}^5(x_i{)}^2+(-50{)}^2}{6}-\left({\sum }_{i=1}^5\frac{x_i-50}{6}\right)$
$=507.5$