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

....... is a branch of Mathematics in which the extraction of meaningful information is studied.

To draw a histogram to represent the following frequency distribution:

Class interval	$5-10$	$10-15$	$15-25$	$25-45$	$45-75$
Frequency	$6$	$12$	$10$	$8$	$15$

The adjusted frequency for the class $25-45$ is:

$A$ football player scored the following number of goals in $10$ matches:
$1, 3, 2, 5, 8, 6, 1, 4, 7, 9$
Since the number of matches is $10$ (an even number),the median is calculated as:
Median $= \frac{5^{\text{th}} \text{ observation} + 6^{\text{th}} \text{ observation}}{2}$
$= \frac{8 + 6}{2} = 7$
Is this the correct answer? If not,why?

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.

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