For a given frequency distribution,$A=49.5, \Sigma f_{i}=40, \Sigma f_{i} u_{i}=-5$ and $c=20$. Then,mean $\bar{x}=$ ............

The mean of ungrouped data and the mean calculated when the same data is grouped are always the same. Do you agree with this statement? Give reason for your answer.

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

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

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.

Find the median of the following frequency distribution:

Class	$5-10$	$10-15$	$15-20$	$20-25$	$25-30$	$30-35$	$35-40$	$40-45$
Frequency	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$