For a given frequency distribution,$n=100, A=15$ and $\bar{x}=15$. Then,$\Sigma f_{i} d_{i} = \ldots$

Find the mean of the distribution:

Class	$1-3$	$3-5$	$5-7$	$7-10$
Frequency	$9$	$22$	$27$	$17$

In the formula $M = l + \frac{(\frac{n}{2} - cf)}{f} \times h$ for the median,$h = \ldots \ldots \ldots$

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	$12$	$30$	$x$	$65$	$y$	$25$	$18$

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.

If the mean of $12, 13, x, 17, 18$ and $20$ is $16,$ then $x = \ldots \ldots \ldots \ldots .$