For some given data,if $M + \bar{x} = 165$ and $M - \bar{x} = 1$,then $Z = \dots$

$\Sigma(x_{i} - \bar{x}) = \ldots \ldots \ldots$

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.

Find the mode of the following frequency distribution:

Class	$0-100$	$100-200$	$200-300$	$300-400$	$400-500$	$500-600$
Frequency	$7$	$21$	$37$	$13$	$12$	$10$

Find the mean,median and mode of the following frequency distribution:

Class	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$
Frequency	$8$	$15$	$16$	$20$	$12$	$9$

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	$17$	$f_1$	$32$	$f_2$	$19$