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

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 $n$?

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.

The median of a set of $9$ distinct observations is $20.5$. If each of the largest $4$ observations of the set is increased by $2$,then the median of the new set:

The average of $n$ numbers $x_1, x_2, x_3, ..., x_n$ is $M$. If $x_n$ is replaced by $x'$,then the new average is: