If $\bar{x}$ represents the mean of $n$ observations $x_{1}, x_{2}, \ldots, x_{n},$ then the value of $\sum_{i=1}^{n}(x_{i}-\bar{x})$ is

The number of books in different shelves of a library are as follows:
$37, 22, 24, 27, 28, 27, 20, 36, 21, 20,$
$29, 30, 29, 36, 30, 25, 27, 32, 24, 28,$
$34, 20, 25, 28, 30, 20, 35, 25, 27, 31$
Represent the data given above by a grouped frequency distribution table,taking the class intervals as $18-22, 22-26, 26-30, 30-34, 34-38$.

The information regarding the marks scored by $30$ students in a $50$ marks test is given below:

Marks $(x_{i})$	$15$	$22$	$28$	$31$	$35$	$40$	$44$	$46$
Number of students $(f_{i})$	$2$	$3$	$5$	$6$	$6$	$4$	$3$	$1$

Find the mean of the data.

Draw a histogram of the following distribution:

Heights (in $cm$)	Number of students
$150-153$	$7$
$153-156$	$8$
$156-159$	$14$
$159-162$	$10$
$162-165$	$6$
$165-168$	$5$

Draw a histogram for the following frequency distribution with unequal class length:

Class	$0-5$	$5-10$	$10-20$	$20-30$	$30-50$	$50-70$	$70-100$
Frequency	$6$	$8$	$14$	$16$	$24$	$20$	$30$

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.