If the sum of $25$ observations is $900$, find the mean of those observations.

The following are the marks (out of $100$) of $60$ students in mathematics:
$16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28, 72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63, 25, 36, 54, 44, 47, 27, 72, 17, 4, 30$
Construct a grouped frequency distribution table with a width of $10$ for each class,starting from $0-9$.

Find the mean of the following frequency distribution:

Score $(x)$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Frequency $(f)$	$5$	$9$	$12$	$17$	$14$	$10$	$6$

If the mean of the observations $x, x+3, x+5, x+7, x+10$ is $9,$ find the mean of the last three observations.

$30$ 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.

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 $5$.