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 class width of $10$,such that one of the classes is $10-20$ ($20$ not included).

Find the number of observations,if the sum of some observations is $975$ and their mean is $32.5$.

In a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?

The marks obtained (out of $100$ marks) by $50$ students in a mathematics test are as given below:
$\begin{array}{lrrrrrrrrr} 10, & 65, & 75, & 37, & 8, & 58, & 35, & 42, & 29, & 52 \\ 19, & 52, & 23, & 61, & 88, & 65, & 18, & 77, & 85, & 49, \\ 12, & 7, & 41, & 75, & 52, & 90, & 30, & 89, & 95, & 62, \\ 16, & 61, & 35, & 68, & 22, & 72, & 56, & 27, & 62, & 93, \\ 25, & 59, & 48, & 81, & 26, & 84, & 60, & 39, & 76, & 50 \end{array}$
Represent the data given above by a grouped frequency distribution table,taking the class intervals as $0-10, 10-20, \dots$ etc.

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

If each observation of the data is increased by $5,$ then their mean