Question

Statement - $1$: If $\sum _{i=1}^9(x_i-8)=9$ and $\sum _{i=1}^9(x_i-8{)}^2=45$ then $S.D.$ of $x_1,x_2,.....,x_9$ is $2$.
Statement - $2$: S.D. is independent of change of origin.

• A. Both the statements are true
• B. Statement-I is true, but Statement-II is false
• C. Statement-I is false, but Statement-II is true
• D. Both the statements are false

Answer 1

Answer: (A)

Both the statements are true

Statement 1:

Given ${\sum }_{i=1}^9(x_i-8)=9,{\sum }_{i=1}^9(x_i-8{)}^2=45$

$\therefore S.D.=\sqrt{\frac{45}{9}-\frac{9}{9}}=\sqrt{5-1}=\sqrt{4}=2$

Hence Statement 1 is true.

Statement 2:

True. Its value remains same if each item of series is increased or decreased by the constant say $k$. Therefore S.D. is independent of change of origin.

Hence both statements are true.