Question

It was found that an observation $8$ was incorrect, this is observation is now omitted. Find the new standard deviation.

• A. $1.911$
• B. $1.997$
• C. $2.454$
• D. None of the above

Answer 1

Answer: (B)

$1.997$

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 $u^{\prime }=\frac{(\sum x_i)-8}{19}=\frac{192}{19}$
Thus, $u^{\prime }=10.105$.
So, correct variance ${\sigma }^{\prime 2}=\frac{1}{19}(\sum x_i^2-64)-u^{\prime 2}$
$\therefore {\sigma }^{\prime 2}=\frac{1440}{361}$
Thus, $S.D=\sqrt{{\sigma }^2}$
So, $S.D=1.997$
Ans-Option $B$.