$Z - M = \ldots \ldots \ldots \times (M - \bar{x})$

The following are the ages of $300$ patients getting medical treatment in a hospital on a particular day:

Age (in years)	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
Number of patients	$60$	$42$	$55$	$70$	$53$	$20$

Form:
$(i)$ Less than type cumulative frequency distribution.
$(ii)$ More than type cumulative frequency distribution.

For some given data,if $Z - M = 2$ and $\bar{x} = 33.5$,then $Z = \ldots \ldots \ldots$ (in $.5$)

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 data is $55.5$ and the total frequency is $20$. Find the missing frequencies $x$ and $y$.

Class	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$3$	$x$	$7$	$7$	$y$

Will the median class and modal class of grouped data always be different? Justify your answer.