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

Find the mean of the following frequency distribution:

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$2$	$4$	$10$	$20$	$18$	$20$	$16$	$10$

In the formula $Z = l + \left( \frac{f_{1} - f_{0}}{2f_{1} - f_{0} - f_{2}} \right) \times c$ for the mode,$f_{1} = \ldots \ldots \ldots$

In the formula $\bar{x} = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$ for finding the mean of grouped data,$d_{i}$ are deviations from $a$ of:

In calculating the mean of grouped data,grouped in classes of equal width,we may use the formula $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$,where $a$ is the assumed mean. $a$ must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

The median of the following frequency distribution is $46$ and the total frequency is $230$. Find the missing frequencies $x$ and $y$.

Class	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$12$	$30$	$x$	$65$	$y$	$25$	$18$