Find the median for the following distribution:

Class	Frequency
$10-20$	$180$
$20-30$	$82$
$30-40$	$34$
$40-50$	$180$
$50-60$	$136$
$60-70$	$23$
$70-80$	$50$

If the mean of $n$ observations $1^2, 2^2, 3^2, \dots, n^2$ is $\frac{46n}{11}$,then what is the value of $n$?

If the arithmetic mean of the numbers $x_1, x_2, x_3, ..., x_n$ is $\bar{x}$,then the arithmetic mean of the numbers $ax_1 + b, ax_2 + b, ax_3 + b, ..., ax_n + b$,where $a$ and $b$ are two constants,would be:

If a variable takes the discrete values $\alpha - 4, \alpha - \frac{7}{2}, \alpha - \frac{5}{2}, \alpha - 3, \alpha - 2, \alpha + \frac{1}{2}, \alpha - \frac{1}{2}, \alpha + 5$ (where $\alpha > 0$),then the median is:

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	$12$	$8$	$4$	$4$	$3$	$3$	$7$

Find the arithmetic mean of the following frequency distribution.

$x_i$	$5$	$8$	$11$	$14$	$17$
$f_i$	$4$	$5$	$6$	$10$	$20$