Find the mean of the observations $15, 22, 18, 27, 31, 21, 14, 36, 25$ and $34$.

Draw a histogram to represent the following grouped frequency distribution:

Ages (in years)	Number of teachers
$20-24$	$10$
$25-29$	$28$
$30-34$	$32$
$35-39$	$48$
$40-44$	$50$
$45-49$	$35$
$50-54$	$12$

Is it correct to say that in a histogram,the area of each rectangle is proportional to the class size of the corresponding class interval? If not,correct the statement.

If the information gathered by an investigator is from an already existing source of data,then such information is called .........

The scores (out of $100$) obtained by $33$ students in a mathematics test are as follows:
$69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84$
$66, 64, 71, 64, 66, 69, 66, 83, 66, 69, 71$
$81, 71, 73, 69, 66, 66, 64, 58, 64, 69, 69$
Represent this data in the form of a frequency distribution table.

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.