The mean of the following frequency distribution is $43.75$. Find the missing frequency $f$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$	$80-90$	$90-100$
Frequency	$8$	$4$	$20$	$45$	$64$	$32$	$f$	$8$	$2$	$2$

The marks obtained by $30$ students of Class $X$ of a certain school in a Mathematics paper consisting of $100$ marks are presented in the table below. Find the mean of the marks obtained by the students.

Marks obtained $(x_{i})$	$10, 20, 36, 40, 50, 56, 60, 70, 72, 80, 88, 92, 95$
Number of students $(f_{i})$	$1, 1, 3, 4, 3, 2, 4, 4, 1, 1, 2, 3, 1$

Calculate the mean of the frequency distribution of the marks scored by $100$ students in a mathematics test:

Marks	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
No. of students	$20$	$10$	$20$	$30$	$20$

The following distribution gives the daily income of $50$ workers of a factory.

Daily income (in Rs.)	$100-120$	$120-140$	$140-160$	$160-180$	$180-200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Convert the distribution above to a less than type cumulative frequency distribution,and draw its ogive.

The mean of $15$ observations is $16$. If $2$ is added to each observation and then each result is divided by $3$,the new mean is:

In a retail market,fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying numbers of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes	$50$-$52$	$53$-$55$	$56$-$58$	$59$-$61$	$62$-$64$
Number of boxes	$15$	$110$	$135$	$115$	$25$

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?