$\begin{array}{1 1}(A)\;10.10,1.99\\(B)\;8.4,5.6\\(C)\;3,8\\(D)\;20,3.03\end{array} $

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Given , number of observations =100

Mean $\bar {x}=20$

Standard deviation $\sigma=3$

Step 1:

$\therefore \large\frac{\sum x_i}{n}$$ =\bar {x}$

$\qquad= \large\frac{\sum x_i}{100} $$=20$

$\qquad= \sum x_i =2000$

The incorrect observations $21,21$ and $18$ are omitted.

$\therefore$ Correct mean of 97 observations

$\qquad= \large\frac{1940}{97} $$=20$

Step 2:

Standard deviation $\sigma=3$

=> $ \sqrt {\large\frac{\sum x_i^2}{n} - \bigg( \large\frac{\sum x_i}{n}\bigg)^2}$$=\sigma$

$\sqrt {\large\frac{\sum x_i ^2}{100 }- \normalsize (20)^2}=3$

$ \large\frac{\sum x_i^2}{100} $$-400 =9$

$\large\frac{\sum x_i^2}{100} $$=409$

=> $\sum x_i^2 =40900$

By omitting the correct observations 21,21,18

$\sum x+i^2 =40900 -(21)^2 -(21)^2-(18)^2$

$\qquad= 40900 -441-441-324$

$\qquad= 39694$

Correct Standard deviation of 97 observations

$\sigma= \sqrt { \large\frac{39694}{97} - \bigg( \large\frac{1940}{97} \bigg)^2}$

$\qquad= \sqrt {409.2 -(20)^2}$

$\qquad= \sqrt { 409.2 -400 }$

$\qquad= \sqrt {9.2}$

$\qquad= 3.03$

Hence D is the correct answer.

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