# Find the mean and variance of the frequency distribution given below:

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

Toolbox:
• 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.