Find the mode of the following marks (out of $10$) obtained by $20$ students:
$4, 6, 5, 9, 3, 2, 7, 7, 6, 5, 4, 9, 10, 10, 3, 4, 7, 6, 9, 9$

$A$ 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 $2 - 2.5$.

Consider the marks obtained by $10$ students in a mathematics test as given below:
$55, 36, 95, 73, 60, 42, 25, 78, 75, 62$

Give one example of a situation in which $(i)$ the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Consider the marks obtained (out of $100$ marks) by $30$ students of Class $IX$ of a school:
$\begin{array}{*{20}{c}}
{10}&{20}&{36}&{92}&{95}&{40}&{50}&{56}&{60}&{70} \\
{92}&{88}&{80}&{70}&{72}&{70}&{36}&{40}&{36}&{40} \\
{92}&{40}&{50}&{50}&{56}&{60}&{70}&{60}&{60}&{88}
\end{array}$

The 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?