Find the mode of the following observations: $14, 25, 28, 29, 17, 14, 19, 22, 14, 30, 16, 28, 14, 25$.

Two sections of Class $IX$ having $30$ students each appeared for a mathematics olympiad. The marks obtained by them are shown below:
$\begin{array}{lllllllllllllll}46 & 31 & 74 & 68 & 42 & 54 & 14 & 61 & 83 & 48 & 37 & 26 & 8 & 64 & 57 \\ 93 & 72 & 53 & 59 & 38 & 16 & 88 & 75 & 56 & 46 & 66 & 45 & 61 & 54 & 27 \\ 27 & 44 & 63 & 58 & 43 & 81 & 64 & 67 & 36 & 49 & 50 & 76 & 38 & 47 & 55 \\ 77 & 62 & 53 & 40 & 71 & 60 & 58 & 45 & 42 & 34 & 46 & 40 & 59 & 42 & 29\end{array}$
Construct a grouped frequency distribution table for the data above using the classes $0-9, 10-19$,etc.,and hence find the number of students who secured more than $49$ marks.

If the mean of the following data is $20.2,$ find the value of $p:$
$\begin{array}{|c|c|c|c|c|c|} \hline x & 10 & 15 & 20 & 25 & 30 \\ \hline f & 6 & 8 & p & 10 & 6 \\ \hline \end{array}$

The mean of the observations $x+5$,$x+3$,$x+11$,and $x+1$ is ..........

The mean of $10$ observations is calculated as $22.7$. It was later noticed that one observation was taken as $15$ instead of $51$ by mistake. Then,the correct mean of the data is ........

$30$ 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.