The mean of $3, -3, -3, 3, 3, -3$ is ..........

Find the mean,the median,and the mode of the observations:
$33, 92, 55, 90, 35, 77, 58, 41, 80, 64, 46$

The mean of the data: $2, 8, 6, 5, 4, 5, 6, 3, 6, 4, 9, 1, 5, 6, 5$ is given to be $5$. Based on this information,is it correct to say that the mean of the data: $10, 12, 10, 2, 18, 8, 12, 6, 12, 10, 8, 10, 12, 16, 4$ is $10$? Give reason.

The width of the class $50.5-55.5$ is .............

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.

There are $50$ numbers. Each number is subtracted from $53$ and the mean of the numbers so obtained is found to be $-3.5$. The mean of the given numbers is: (in $.5$)