$\begin{array}{1 1}(A)\;4.15,3.049\\(B)\;25,1600\\(C)\;790,87\\(D)\;5.975,2.85\end{array} $

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- The formula to solve this problem:
- Mean $(\bar {x} )=A+\large\frac{\sum f_id_i}{\sum f_i}$
- Standard deviation (SD) $=\sqrt {\large\frac{\sum f_id_i^2}{\sum f_i}- \bigg(\large\frac{\sum f_id_ui}{\sum f_i} \bigg)^2}$

Step 2:

Mean $(\bar {x} )=A+\large\frac{\sum f_id_i}{\sum f_i}$

$\qquad= 9+\large\frac{-121}{40}$

$\qquad= 9- 3.025$

$\qquad= 5.975$

Step 3:

Standard deviation (SD) $=\sqrt {\large\frac{\sum f_id_i^2}{\sum f_i}- \bigg(\large\frac{\sum f_id_ui}{\sum f_i} \bigg)^2}$

$\qquad= \sqrt { \large\frac{691}{40} -\bigg(\large\frac{-121}{40}\bigg)^2}$

$\qquad= \large\frac{1}{40} $$\sqrt {27640 -14641}$

$\qquad=\large\frac{1}{40}$$ \sqrt {12999}$

$\qquad= \large\frac{114.013}{40}$

$\qquad= 2.85$

Hence D is the correct answer.

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