$A$ student was asked to find the arithmetic mean of the numbers $3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14$ and $x$. He found the mean to be $12$. What should be the number in place of $x$?

The average of the first $25$ numbers is $10$ and the average of the next $25$ numbers is $12$. The average of all $50$ numbers is:

The average of a collection of $20$ measurements was calculated to be $56 \, cm$. But later,it was found that a mistake had occurred in one of the measurements which was recorded as $64 \, cm$,but should have been $61 \, cm$. The correct average must be? (in $cm$)

The average of five consecutive positive integers is $n$. If the next two integers are also included,the average of all these integers will

The average age of $30$ girls is $13$ years. The average age of the first $18$ girls is $15$ years. Find the average age of the remaining $12$ girls.

The average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).