Question

The mean and the standard deviation( $s.d$.) of five observations are $9$ and $0$, respectively. If one of the observations 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. 2
• D. 4

Answer 1

Answer: (C)

In the first case, Mean of 5 observations $=9$
Standard Deviation $=0$
Since, standard deviation is 0, all the five observations remain the same having value of mear n 9
That is, 5 observations $=9,9,9,9,9$
In the second case,
One of the observations is changed so that mean becomes 10 , that is,
$\frac{9+9+9+9+x}{5}=10$
$36+x=50$
$x=14$
Now,

observations (x)	Mean $\overline{(x)}$	$(x-\bar{x})$	$(x-\bar{x}{)}^2$
9	10	-1	1
9	10	-1	1
9	10	-1	1
9	10	-1	1
14	10	4	16

Therefore, s.d. $=\sqrt{\frac{(x-\bar{x}{)}^2}{n}}$
$=\sqrt{\frac{20}{5}}$
$=\sqrt{4}=2$