The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre,and the data obtained is represented in the following table:

Length (in mm)	Number of leaves
$118-126$	$3$
$127-135$	$5$
$136-144$	$9$
$145-153$	$12$
$154-162$	$5$
$163-171$	$4$
$172-180$	$2$

Find the median length of the leaves.

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 marks distribution of $30$ students in a mathematics examination is given in the table. Find the mode of this data. Also,compare and interpret the mode and the mean.

Class interval	$10-25$	$25-40$	$40-55$	$55-70$	$70-85$	$85-100$
Number of students	$2$	$3$	$7$	$6$	$6$	$6$

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.

Weight (in kg)	$40-45$	$45-50$	$50-55$	$55-60$	$60-65$	$65-70$	$70-75$
Number of students	$2$	$3$	$8$	$6$	$6$	$3$	$2$

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher	Number of states/$U$.$T$.
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

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:
$\begin{array}{|c|c|} \hline \text{Expenditure (in Rs)} & \text{Number of families} \\ \hline 1000-1500 & 24 \\ 1500-2000 & 40 \\ 2000-2500 & 33 \\ 2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7 \\ \hline \end{array}$