$\sum_{i=1}^{10} (x_i - \bar{x}) = \dots$

$A$ class teacher has the following absentee record of $40$ students of a class for the whole term. Find the mean number of $days$ a student was absent.
$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text{Number of days} & 0-6 & 6-10 & 10-14 & 14-20 & 20-28 & 28-38 & 38-40 \\ \hline \text{Number of students} & 11 & 10 & 7 & 4 & 4 & 3 & 1 \\ \hline \end{array}$

The mean of the following frequency distribution is $65$ and the total frequency is $100$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class	$15-35$	$35-55$	$55-75$	$75-95$	$95-115$
Frequency	$17$	$f_1$	$32$	$f_2$	$19$

For a given frequency distribution,$\Sigma f_{i} u_{i} = -13$,$n = \Sigma f_{i} = 100$,$A = 62.5$ and $c = 15$. Then,mean $\bar{x} = \dots$

The mean of the following frequency distribution is $52$. Find the missing frequency $f$.

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$5$	$3$	$4$	$f$	$2$	$6$	$13$

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is $Rs. 18$. Find the missing frequency $f$.

Daily pocket allowance (in $Rs.$)	$11-13$	$13-15$	$15-17$	$17-19$	$19-21$	$21-23$	$23-25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$