Find the median for the following distribution:

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

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?

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.

The mean marks of $100$ students in a class in mathematics is $72$. If the number of boys is $70$ and their mean marks is $75$,find the mean marks of the girls in the class.

If four different subjects are assigned weights in an examination as Physics $(2)$,Chemistry $(1)$,English $(1)$,and Mathematics $(2)$,and a student scores $60$ in Physics,$70$ in Chemistry,$70$ in English,and $80$ in Mathematics,find the weighted mean.

In a data,if the number $i$ is repeated $i$ times for $i=1, 2, \ldots, n$,then the mean of the data is