Question

If both the standard deviation and mean of data set $x_1,x_2,x_3,....x_{50}$ are $16$. Then the mean of the data seg $(x_1-4{)}^2,(x_2-4{)}^2,(x_3-4{)}^2,.....(x_{50}-4{)}^2$ is?

• A. $200$
• B. $100$
• C. $400$
• D. $1600$

Answer 1

Answer: (C)

$400$

$\sum \frac{x_i}{50}=16$
Variance $=256$
Variance remains same for $(x_i-4)$ data set
$\therefore {\sigma }^2=\frac{1}{50}\sum (x_i-4{)}^2-(16-4{)}^2=256\Rightarrow \frac{1}{50}\sum (x_i-4{)}^2=400$
$\therefore$ Mean of $(x_1-4{)}^2,(x_2-4{)}^2,....(x_{50}-4{)}^2$ is $\frac{\sum (x_i-4{)}^2}{50}=400$.