$\begin{array}{1 1}(A)\;4.15,3.049\\(B)\;25,1600\\(C)\;790,87\\(D)\;153,45\end{array} $

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- The formula used to solve this problem are :
- Mean $(\bar {x} )=\large\frac{\sum f_ix_i}{\sum f_i}$
- Variance $\sigma^2= \large\frac{\sum f_i (x_i - \bar {x} )^2}{\sum f_i}$

Step 2:

Mean $(\bar {x} )=\large\frac{\sum f_ix_i}{\sum f_i}$

$\qquad= \large\frac{66.5}{16}$$=4.15$

Step 3:

Variance $\sigma^2= \large\frac{\sum f_i (x_i - \bar {x} )^2}{\sum f_i}$

$\qquad= \large\frac{48.785}{16}$

$\qquad= 3.049$

Hence A is the correct answer.

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