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:

Find the mean of the following frequency distribution:

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

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 $n$?

In a class of $100$ students,there are $70$ boys whose average marks in a subject are $75$. If the average marks of the complete class are $72$,then what are the average marks of the girls?

For a distribution $x_1, x_2, \dots, x_{101}$ such that $x_1 < x_2 < x_3 < \dots < x_{100} < x_{101}$,the mean deviation of this distribution about a number $k$ is minimum. Then $k$ is equal to which of the following?

$x_1, x_2, \dots, x_{34}$ are numbers such that $x_i = 150$ for all $i \in \{1, 2, \dots, 10\}$ and $x_{i+1} - x_i = -2$ for all $i \in \{10, 11, \dots, 33\}$. Find the median of $x_1, x_2, \dots, x_{34}$.