Find the mean of the marks obtained by $30$ students of Class $IX$ of a school.
$\begin{array}{llllllllll}10 & 20 & 36 & 92 & 95 & 40 & 50 & 56 & 60 & 70 \\ 92 & 88 & 80 & 70 & 72 & 70 & 36 & 40 & 36 & 40 \\ 92 & 40 & 50 & 50 & 56 & 60 & 70 & 60 & 60 & 88\end{array}$

The distances (in $km$) of $40$ engineers from their residence to their place of work were found as follows:

$5$	$3$	$10$	$20$	$25$	$11$	$13$	$7$	$12$	$31$
$19$	$10$	$12$	$17$	$18$	$11$	$32$	$17$	$16$	$2$
$7$	$9$	$7$	$8$	$3$	$5$	$12$	$15$	$18$	$3$
$12$	$14$	$2$	$9$	$6$	$15$	$15$	$7$	$6$	$12$

Construct a grouped frequency distribution table with class size $5$ for the data given above,taking the first interval as $0-5$ ($5$ not included). What main features do you observe from this tabular representation?

$100$ 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.

Give one example of a situation in which $(i)$ the mean is an appropriate measure of central tendency.

$A$ company manufactures car batteries of a particular type. The lives (in years) of $40$ such batteries were recorded as follows:
$\begin{array}{llllllll}2.6 & 3.0 & 3.7 & 3.2 & 2.2 & 4.1 & 3.5 & 4.5 \\ 3.5 & 2.3 & 3.2 & 3.4 & 3.8 & 3.2 & 4.6 & 3.7 \\ 2.5 & 4.4 & 3.4 & 3.3 & 2.9 & 3.0 & 4.3 & 2.8 \\ 3.5 & 3.2 & 3.9 & 3.2 & 3.2 & 3.1 & 3.7 & 3.4 \\ 4.6 & 3.8 & 3.2 & 2.6 & 3.5 & 4.2 & 2.9 & 3.6\end{array}$
Construct a grouped frequency distribution table for this data,using class intervals of size $0.5$ starting from the interval $2 - 2.5$.

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?