Find the arithmetic mean of the following frequency distribution.

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

What is the weighted mean of the first $n$ natural numbers if the weights are equal?

The mean of a set of $n$ numbers,when each is divided by $5$,is $\frac{X}{5}$. What is the mean of the original $n$ numbers?

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

The mean of a set of observations is $\bar{x}$. If each observation is divided by $\alpha$ $(\alpha \neq 0)$ and then increased by $10$,what is the mean of the new set?

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: