Question

It was found that an observation $8$ was incorrect, this is observation is now replaced by an observation $12$. Find the new standard deviation:

• A. $2.533$
• B. $3.232$
• C. $1.379$
• D. $1.989$

Answer 1

Answer: (D)

$1.989$

Mean $=10\Rightarrow \frac{\sum x_i}{20}=10$
$\therefore \sum x_i=200$
$SD=2\Rightarrow {\sigma }^2=4$
$\therefore \frac{\sum x_i^2}{20}-{10}^2=4$
Thus, $\sum x_i^2=2080$.
So, correct mean $u^{\prime }=\frac{(\sum x_i)-8+12}{20}=\frac{204}{20}$
Thus, $u^{\prime }=10.2$.
So, correct variance ${\sigma }^{\prime 2}=\frac{1}{20}(\sum x_i^2-8^2+{12}^2)-u^{\prime 2}$
$\therefore {\sigma }^{\prime 2}=3.96$
Thus, $S.D=\sqrt{{\sigma }^2}$
So, $S.D=1.989$
Ans-Option $D$.