The table below gives the percentage distribution of female teachers in the primary schools of rural areas of various states and union territories $(U.T.)$ of India. Find the mean percentage of female teachers by all the three methods discussed in this section.

Percentage of female teachers	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$	$65$-$75$	$75$-$85$
Number of States/$U$.$T$.	$6$	$11$	$7$	$4$	$4$	$2$	$1$

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?

The following data gives the distribution of total monthly household expenditure of $200$ families of a village. Find the modal monthly expenditure of the families. Also,find the mean monthly expenditure:
$\begin{array}{|c|c|} \hline \text{Expenditure (in Rs)} & \text{Number of families} \\ \hline 1000-1500 & 24 \\ 1500-2000 & 40 \\ 2000-2500 & 33 \\ 2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7 \\ \hline \end{array}$

The median of the following data is $525$. Find the values of $x$ and $y$,if the total frequency is $100$.

Class interval	Frequency
$0-100$	$2$
$100-200$	$5$
$200-300$	$x$
$300-400$	$12$
$400-500$	$17$
$500-600$	$20$
$600-700$	$y$
$700-800$	$9$
$800-900$	$7$
$900-1000$	$4$

The table below shows the daily expenditure on food of $25$ households in a locality.

Daily expenditure (in $Rs.$)	$100-150$	$150-200$	$200-250$	$250-300$	$300-350$
Number of households	$4$	$5$	$12$	$2$	$2$

Find the mean daily expenditure on food by a suitable method.

The following table gives the production yield per hectare of wheat of $100$ farms of a village.

Production yield (in kg/ha)	Number of farms
$50-55$	$2$
$55-60$	$8$
$60-65$	$12$
$65-70$	$24$
$70-75$	$38$
$75-80$	$16$

Change the distribution to a 'more than type' distribution,and draw its ogive.