The mean of $35$ observations is $42$. Find the sum of those observations $\left(\Sigma f_{i} x_{i}\right)$.

State whether each of the following statements is true or false:
$(1)$ The median of the observations $12, 13, 14, 15, 16$ is $14$.
$(2)$ The mode of the observations $1, 3, 5, 7, 9$ is $5$.

The mean of the data $\frac{4}{7}, \frac{4}{9}, \frac{3}{7}, \frac{5}{9}$ is ........

If the mean of the following data is $20.2,$ find the value of $p:$
$\begin{array}{|c|c|c|c|c|c|} \hline x & 10 & 15 & 20 & 25 & 30 \\ \hline f & 6 & 8 & p & 10 & 6 \\ \hline \end{array}$

The information regarding the marks scored by $30$ students in a $50$ marks test is given below:

Marks $(x_{i})$	$15$	$22$	$28$	$31$	$35$	$40$	$44$	$46$
Number of students $(f_{i})$	$2$	$3$	$5$	$6$	$6$	$4$	$3$	$1$

Find the mean of the data.

The mean marks (out of $100$) of boys and girls in an examination are $70$ and $73$,respectively. If the mean marks of all the students in that examination is $71$,find the ratio of the number of boys to the number of girls.