The average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).

$16$ children are to be divided into two groups $A$ and $B$ of $10$ and $6$ children,respectively. The average marks obtained by the children of group $A$ is $75$ and that of all the children is $76$. Then,the average marks of the children of group $B$ is?

The batting average of a cricket player for $64$ innings is $62$ runs. His highest score exceeds his lowest score by $180$ runs. Excluding these two innings,the average of the remaining innings becomes $60$ runs. His highest score was (in $Runs$):

The average age of students of a class is $15.8 \, \text{years}$. The average age of boys in the class is $16.4 \, \text{years}$ and that of the girls is $15.4 \, \text{years}$. The ratio of the number of boys to the number of girls in the class is:

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

In a competitive examination,the average marks obtained was $45$. It was later discovered that there was some error in computerization and the marks of $90$ candidates had to be changed from $80$ to $50$,and the average came down to $40$ marks. The total number of candidates appeared in the examination is