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.

$A$ class has $20$ boys and $30$ girls. The average age of boys is $11$ years and that of girls is $12$ years. What is the average age of the whole class in years?

The average age of $35$ students in a class is $16$ years. The average age of $21$ students is $14$ years. What is the average age of the remaining $14$ students (in years)?

The average weight of $100$ students is $32\, kg$. The average weight of the first $49$ students is $30\, kg$ and that of the last $50$ students is $34\, kg$. What is the weight (in $kg$) of the $50^{th}$ student?

In a family,the average age of father and mother is $38 \text{ years}$,whereas the average age of father,mother,and their only daughter is $28 \text{ years}$. Then,the age of the daughter is? (in $\text{years}$)

In a class,the average height of $35$ girls was measured as $160 \,cm$. Later,it was discovered that the height of one of the girls was misread as $144 \,cm$,while her actual height was $104 \,cm$. What was the actual average height of the girls in the class? (in $cm$) (rounded off to two digits after decimal)