State whether each of the following statements is true or false:
$(1)$ The median of the observations $12, 13, 14, 15, 16$ is $14$.
$(2)$ The mode of the observations $1, 3, 5, 7, 9$ is $5$.

The mean of the $10$ observations is $68$. If each observation is divided by $2$ and then $6$ is added to each result, find the mean of the new observations so obtained.

The marks obtained (out of $100$ marks) by $50$ students in a mathematics test are as given below:
$\begin{array}{lrrrrrrrrr} 10, & 65, & 75, & 37, & 8, & 58, & 35, & 42, & 29, & 52 \\ 19, & 52, & 23, & 61, & 88, & 65, & 18, & 77, & 85, & 49, \\ 12, & 7, & 41, & 75, & 52, & 90, & 30, & 89, & 95, & 62, \\ 16, & 61, & 35, & 68, & 22, & 72, & 56, & 27, & 62, & 93, \\ 25, & 59, & 48, & 81, & 26, & 84, & 60, & 39, & 76, & 50 \end{array}$
Represent the data given above by a grouped frequency distribution table,taking the class intervals as $0-10, 10-20, \dots$ etc.

Draw a histogram of the following distribution:

Heights (in $cm$)	Number of students
$150-153$	$7$
$153-156$	$8$
$156-159$	$14$
$159-162$	$10$
$162-165$	$6$
$165-168$	$5$

$A$ class consists of $50$ students out of which $30$ are girls. The mean of marks scored by girls in a test is $73$ (out of $100$) and that of boys is $71$. Determine the mean score of the whole class.

There are $50$ numbers. Each number is subtracted from $53$ and the mean of the numbers so obtained is found to be $-3.5$. The mean of the given numbers is: (in $.5$)