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

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 temperature for Monday,Tuesday,Wednesday and Thursday was $48^{\circ}$. The average temperature for Tuesday,Wednesday,Thursday and Friday was $52^{\circ}$. If the temperature on Monday was $42^{\circ}$,then the temperature on Friday was (in $degrees$):

$A$ batsman has a certain average of runs for $12$ innings. In the $13^{th}$ innings,he scores $96$ runs,thereby increasing his average by $5$ runs. What is his average after the $13^{th}$ innings?

$A$ motorist covered the first $20 \text{ km}$ of his journey in $30 \text{ minutes}$ and the remaining $29 \text{ km}$ in $40 \text{ minutes}$. His average speed in $\text{km/hr}$ is:

The arithmetic mean of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$. The mean score of the remaining $55\%$ is