The mean of $10$ observations is $52$. If $12$ is subtracted from each observation,then the mean of the new observations so obtained is:

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.

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

$A$ grouped frequency distribution table with classes of equal sizes using $63-72$ ($72$ included) as one of the class is constructed for the following data:
$30, 32, 45, 54, 74, 78, 108, 112, 66, 76, 88$
$40, 14, 20, 15, 35, 44, 66, 75, 84, 95, 96$
$102, 110, 88, 74, 112, 14, 34, 44$
The number of classes in the distribution will be:

$30$ children were asked about the number of hours they watched $TV$ programmes last week. The results are recorded as under:

Number of hours	$0-5$	$5-10$	$10-15$	$15-20$
Frequency	$8$	$16$	$4$	$2$

Can we say that the number of children who watched $TV$ for $10$ or more hours a week is $22$? Justify your answer.

$A$ die is thrown $1000$ times and the outcomes were recorded as follows:

Outcome	$1$	$2$	$3$	$4$	$5$	$6$
Frequency	$180$	$150$	$160$	$170$	$150$	$190$

If the die is thrown once more,then the probability that it shows $5$ is: