Question

The mean and the standard deviation(s.d.) of five observations are $9$ and $0$, respectively. If one of the observation is changed such that the mean of the new set of five observations becomes $10$, then their s.d. is :

• A. $0$
• B. $1$
• C. $4$
• D. $2$

Answer 1

The correct option is D $2$

Since, the standard deviation before the change was 0, hence all the five observations were exactly equal to 9.
Now, one observation is changed and the new mean is 10,
$\Rightarrow \frac{9+9+9+9+x}{5}=10\Rightarrow x=14\therefore S.D.=\sqrt{\frac{(9-10{)}^2+(9-10{)}^2+(9-10{)}^2+(9-10{)}^2+(14-10{)}^2}{5}}=2$