$A$ survey conducted on $20$ households in a locality by a group of students resulted in the following frequency table for the number of family members in a household:

Family size	$1-3$	$3-5$	$5-7$	$7-9$	$9-11$
Number of families	$7$	$8$	$2$	$2$	$1$

Find the mode of this data.

The annual profits earned by $30$ shops of a shopping complex in a locality give rise to the following distribution:

Profit (Rs in lakhs)	Number of shops (frequency)
More than or equal to $5$	$30$
More than or equal to $10$	$28$
More than or equal to $15$	$16$
More than or equal to $20$	$14$
More than or equal to $25$	$10$
More than or equal to $30$	$7$
More than or equal to $35$	$3$

Draw both ogives for the data above. Hence,obtain the median profit.

Consider the following distribution of daily wages of $50$ workers of a factory.
$\begin{array}{|l|c|c|c|c|c|} \hline \text{Daily wages (in Rs.)} & 100-120 & 120-140 & 140-160 & 160-180 & 180-200 \\ \hline \text{Number of workers} & 12 & 14 & 8 & 6 & 10 \\ \hline \end{array}$
Find the mean daily wages of the workers of the factory by using an appropriate method.

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored	Number of batsmen
$3000-4000$	$4$
$4000-5000$	$18$
$5000-6000$	$9$
$6000-7000$	$7$
$7000-8000$	$6$
$8000-9000$	$3$
$9000-10000$	$1$
$10000-11000$	$1$

Find the mode of the data.

During the medical check-up of $35$ students of a class,their weights were recorded as follows:

Weight (in kg)	Number of students
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$

Draw a less than type ogive for the given data. Hence,obtain the median weight from the graph and verify the result by using the formula.

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	$2$	$3$	$8$	$6$	$6$	$3$	$2$