The average of $12$ results is $15,$ and the average of the first two is $14.$ What is the average of the rest?

The average weight of a class of $24$ students is $35 \, kg$. If the weight of the teacher is included, the average weight increases by $400 \, g$. The weight of the teacher is (in $kg$):

$A$ cricketer had a certain average of runs for his $64$ innings. In his $65^{th}$ innings,he is bowled out for no score on his part. This brings down his average by $2$ runs. What is his new average of runs?

The average weight of $45$ students in a class is $52 \, kg.$ Five of them whose average weight is $48 \, kg$ leave the class and other $5$ students whose average weight is $54 \, kg$ join the class. What is the new average weight (in $kg$) of the class?

The mean of $11$ numbers is $35$. If the mean of the first $6$ numbers is $32$ and that of the last $6$ numbers is $37$, then find the sixth number.

The average of $50$ numbers is $38$. If two numbers $45$ and $55$ are discarded,the average of the remaining set of numbers is: