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 median of the sequence $^{2n}C_0, ^{2n}C_1, ^{2n}C_2, \dots, ^{2n}C_n$ (where $n$ is even).

Let $M$ denote the median of the following frequency distribution. Then $20M$ is equal to:

Class	$0-4$	$4-8$	$8-12$	$12-16$	$16-20$
Frequency	$3$	$9$	$10$	$8$	$6$

Find the weighted mean of the first $n$ natural numbers,where the weights are equal to their squares.

Which formula is used to calculate the weighted mean?

The average age of a teacher and three students is $20$ years. If all the students are of the same age and the difference between the teacher's age and the age of one of the students is $20$ years,find the teacher's age in years.