In the formula $\bar{x} = \frac{\Sigma f_{i} x_{i}}{\Sigma f_{i}}$,$\Sigma f_{i}$ represents ........

The formula to find the median of a grouped data is $\ldots \ldots \ldots \ldots .$

In calculating the mean of grouped data,grouped in classes of equal width,we may use the formula $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$,where $a$ is the assumed mean. $a$ must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

The percentage of marks obtained by $100$ students in an examination are given below:

Marks	$30-35$	$35-40$	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$
Frequency	$14$	$16$	$18$	$23$	$18$	$8$	$3$

Determine the median percentage of marks.

The mean of the following frequency distribution is $28.5$ and the total frequency is $60$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$6$	$f_1$	$20$	$15$	$f_2$	$4$

The mode of the following data is $33 \frac{1}{3}$ and the total frequency is $100$. Find the missing frequencies $x$ and $y$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$7$	$12$	$x$	$28$	$y$	$9$