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.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$10$	$12$	$13$	$16$	$9$

For the frequency distribution given above,which of the following is false?

For some given data,if $\bar{x} + Z = 37.5$ and $\bar{x} - Z = 1.5$,then $M = \ldots$

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

If $Z+M=34$ and $M+\bar{x}=40,$ then $M=\ldots \ldots \ldots . . .$

The following data gives the distribution of total monthly household expenditure of $200$ families of a village. Find the modal monthly expenditure of the families. Also,find the mean monthly expenditure:
$\begin{array}{|c|c|} \hline \text{Expenditure (in Rs)} & \text{Number of families} \\ \hline 1000-1500 & 24 \\ 1500-2000 & 40 \\ 2000-2500 & 33 \\ 2500-3000 & 28 \\ 3000-3500 & 30 \\ 3500-4000 & 22 \\ 4000-4500 & 16 \\ 4500-5000 & 7 \\ \hline \end{array}$