$100$ surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters	Number of surnames
$1-4$	$6$
$4-6$	$30$
$6-8$	$44$
$8-12$	$16$
$12-20$	$4$

$(i)$ Draw a histogram to depict the given information.
$(ii)$ Write the class interval in which the maximum number of surnames lie.

Find the mean salary of $60$ workers of a factory from the following table:

Salary (in Rs.)	Number of workers
$3000$	$16$
$4000$	$12$
$5000$	$10$
$6000$	$8$
$7000$	$6$
$8000$	$4$
$9000$	$3$
$10000$	$1$
Total	$60$

Van Mahotsava was celebrated in $100$ schools,where $100$ plants were planted in each school. After one month,the number of plants that survived were recorded as follows:
$\begin{array}{llllllllll}95 & 67 & 28 & 32 & 65 & 65 & 69 & 33 & 98 & 96 \\ 76 & 42 & 32 & 38 & 42 & 40 & 40 & 69 & 95 & 92 \\ 75 & 83 & 76 & 83 & 85 & 62 & 37 & 65 & 63 & 42 \\ 89 & 65 & 73 & 81 & 49 & 52 & 64 & 76 & 83 & 92 \\ 93 & 68 & 52 & 79 & 81 & 83 & 59 & 82 & 75 & 82 \\ 86 & 90 & 44 & 62 & 31 & 36 & 38 & 42 & 39 & 83 \\ 87 & 56 & 58 & 23 & 35 & 76 & 83 & 85 & 30 & 68 \\ 69 & 83 & 86 & 43 & 45 & 39 & 83 & 75 & 66 & 83 \\ 92 & 75 & 89 & 66 & 91 & 27 & 88 & 89 & 93 & 42 \\ 53 & 69 & 90 & 55 & 66 & 49 & 52 & 83 & 34 & 36\end{array}$

Consider the marks,out of $100$,obtained by $51$ students of a class in a test,given in the table below. Draw a frequency polygon corresponding to this frequency distribution table.

Marks	Number of students
$0-10$	$5$
$10-20$	$10$
$20-30$	$4$
$30-40$	$6$
$40-50$	$7$
$50-60$	$3$
$60-70$	$2$
$70-80$	$2$
$80-90$	$3$
$90-100$	$9$
Total	$51$

Let us consider the following frequency distribution table which gives the weights of $38$ students of a class:

Weights (in $kg$)	Number of students
$31-35$	$9$
$36-40$	$5$
$41-45$	$14$
$46-50$	$3$
$51-55$	$1$
$56-60$	$2$
$61-65$	$2$
$66-70$	$1$
$71-75$	$1$
Total	$38$

If two new students of weights $35.5\, kg$ and $40.5\, kg$ are admitted to this class,how should the frequency distribution table be adjusted to include them?

The heights of $50$ students,measured to the nearest centimetres,have been found to be as follows:
$\begin{array}{llllllllll}161 & 150 & 154 & 165 & 168 & 161 & 154 & 162 & 150 & 151 \\ 162 & 164 & 171 & 165 & 158 & 154 & 156 & 172 & 160 & 170 \\ 153 & 159 & 161 & 170 & 162 & 165 & 166 & 168 & 165 & 164 \\ 154 & 152 & 153 & 156 & 158 & 162 & 160 & 161 & 173 & 166 \\ 161 & 159 & 162 & 167 & 168 & 159 & 158 & 153 & 154 & 159\end{array}$
$(i)$ Represent the data given above by a grouped frequency distribution table,taking the class intervals as $150-155, 155-160,$ etc.
$(ii)$ What can you conclude about their heights from the table?