The average weight of $5$ persons,sitting in a boat,is $38 \, kg$. If the average weight of the boat and the persons sitting in the boat is $52 \, kg$,what is the weight of the boat? (in $kg$)

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 $4$ numbers is $64$. If the sum of the squares of the first and the last element is $178$,then the average of all the $6$ numbers is:

The average marks obtained by a class of $60$ students is $65$. The average marks of half of the students is found to be $85$. The average marks of the remaining students is:

In a family,the average age of a father and a mother is $35 \text{ years}$. The average age of the father,mother,and their only son is $27 \text{ years}$. What is the age of the son (in $\text{years}$)?

The mean of $100$ items was $46$. Later on,it was discovered that an item $16$ was misread as $61$ and another item $43$ was misread as $34$. It was also found that the number of items was $90$ and not $100$. What is the correct mean?

The average of $11$ numbers is $10.9$. If the average of the first six is $10.5$ and the average of the last six is $11.4$, find the middle (sixth) number.