Find the arithmetic mean of the following frequency distribution.

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

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

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 of these values is:

If the mean of the numbers $27 + x$,$31 + x$,$89 + x$,$107 + x$,and $156 + x$ is $82$,then the mean of $130 + x$,$126 + x$,$68 + x$,$50 + x$,and $1 + x$ is:

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:

The relation between the median $M$,the second quartile ${Q_2}$,the fifth decile ${D_5}$,and the $50^{th}$ percentile ${P_{50}}$ of a set of observations is: