The average of $n$ numbers $x_{1}, x_{2}, \ldots, x_{n}$ is $x$. Then, the value of $\sum \limits_{i=1}^{n}\left(x_{i}-\bar{x}\right)$ is equal to

In a class of $100$ students, the mean marks obtained in a subject is $30$ and in another class of $50$ students the mean marks obtained in the same subject is $60 .$ The mean marks obtained by the students of two classes taken together is

A man travels by a car to his office at $60 \,km / h$ and returns home along the same route at $20 \,km / h .$ Find the average speed of his whole journey. (in $km/h$)

The average of $5$ consecutive integers starting with $m$ is $n$. What is the average of $6$ consecutive integers starting with $( m +2) ?$

The average age of Sachin and Ganguli is $35 \,years.$ If Kaif replaces Sachin, the average age becomes $32 \,years$ and if Kaif replaces Ganguli, then the average age becomes $38 \,years.$ If the average age of Dhoni and Irfan be half of the average age of Sachin, Ganguli and Kaif, then the average age of all the five people is:

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