$A$ survey regarding the heights (in $cm$) of $51$ girls of Class $X$ of a school was conducted and the following data was obtained:

Height (in $cm$)	Number of girls
Less than $140$	$4$
Less than $145$	$11$
Less than $150$	$29$
Less than $155$	$40$
Less than $160$	$46$
Less than $165$	$51$

Find the median height.

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 distribution below shows the number of wickets taken by bowlers in one-day cricket matches. Find the mean number of wickets by choosing a suitable method. What does the mean signify?

Number of wickets	$20$-$60$	$60$-$100$	$100$-$150$	$150$-$250$	$250$-$350$	$350$-$450$
Number of bowlers	$7$	$5$	$16$	$12$	$2$	$3$

If the median of the distribution given below is $28.5,$ find the values of $x$ and $y$.

Class interval	Frequency
$0-10$	$5$
$10-20$	$x$
$20-30$	$20$
$30-40$	$15$
$40-50$	$y$
$50-60$	$5$
Total	$60$

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	$2$	$3$	$7$	$6$	$6$	$6$