If the mean of the first $n$ natural numbers is equal to $\frac{n + 7}{3}$,then what is the value of $n$?

Let $x_1, x_2, \ldots, x_{11}$ be $11$ distinct positive integers. If we replace the largest of these integers by the median of the other $10$ integers,then:

The arithmetic mean of the following discrete data $12, 14, 20, 23, 25, 32$ is given by

If $\mu$ is the mean of a distribution $(y_i, f_i)$,then $\sum f_i(y_i - \mu) = $

The following data gives the distribution of height of students. The median of the distribution is:

Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

If for some $x \in R$,the frequency distribution of the marks obtained by $20$ students in a test is:
Marks: $2, 3, 5, 7$
Frequency: $(x+1)^2, 2x-5, x^2-3x, x$
Then the mean of the marks is: