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

The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What might be the weight of the new person? (in $kg$)

The average weight of $10$ students is increased by half a $kg$ when one of the students weighing $50\, kg$ is replaced by a new student. Find out the weight of the new student.(in $kg$)

A batsman makes a score of $8$ runs in the $16^{\text {th }}$ match and thus increases his average runs per match by $3 .$ What is his average after the $16^{\text {th }}$ match?

A group of boys has an average weight of $36 \,kg$. One boy weighing $42 \,kg$ leaves the group and another boy weighing $30\, kg$ joints the group. If the average now becomes $35.7\, kg$, then how many boys are there in the group?

There are $6$ consecutive odd numbers in increasing order. The difference between the average of the squares of the first $4$ numbers and the last four numbers is $64 .$ If the sum of the squares of the first and the last element (i.e., odd numbers) is $178 ,$ then the average of all the six numbers is