The marks obtained (out of $50$ marks) by $30$ students in a mathematics test are as given below:
$37, 22, 35, 42, 10, 16, 31, 22, 20, 27$
$27, 20, 31, 40, 35, 40, 27, 16, 47, 22$
$40, 22, 35, 20, 37, 20, 37, 47, 42, 31$
Represent this data in a frequency distribution table.

The mean of $10$ observations is $48$. If each observation is divided by $3$,what will be the new mean?

$A$ grouped frequency table with class intervals of equal sizes using $250-270$ ($270$ not included in this interval) as one of the class intervals is constructed for the following data:
$268, 220, 368, 258, 242, 310, 272, 342$
$310, 290, 300, 320, 319, 304, 402, 318$
$406, 292, 354, 278, 210, 240, 330, 316$
$406, 215, 258, 236$
The frequency of the class $310-330$ is:

Find the number of observations,if the sum of some observations is $975$ and their mean is $32.5$.

The mean of the $10$ observations is $11$. If one new observation is included,their mean becomes $12$. The included new observation is ........

Consider the data $: 2, 3, 9, 16, 9, 3, 9$. Since $16$ is the highest value in the observations,is it correct to say that it is the mode of the data? Give reason.