For some given data,if $M + \bar{x} = 32$ and $M - \bar{x} = 2$,then $Z = \ldots \ldots \ldots$

The mode of the following frequency distribution is $46$ and the total frequency is $150$. Find the missing frequencies $x$ and $y$.

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
Frequency	$6$	$8$	$17$	$x$	$42$	$30$	$y$	$8$

For a given frequency distribution,$A = 450, c = 100, \Sigma f_{i} u_{i} = -20$ and $\Sigma f_{i} = 20$. Then,the mean $\bar{x} = \ldots$

The mean of $5$ observations is $16$. If an observation $5$ is replaced by $-5$,the new mean is ...........

If $Z = 36.8$ and $M = 33.6$,then $\bar{x} = \ldots \ldots \ldots \ldots .$

The times,in seconds,taken by $150$ athletes to run a $110\, m$ hurdle race are tabulated below:

Class (seconds)	$13.8-14.0$	$14.0-14.2$	$14.2-14.4$	$14.4-14.6$	$14.6-14.8$	$14.8-15.0$
Frequency	$2$	$4$	$5$	$71$	$48$	$20$

The number of athletes who completed the race in less than $14.6\, s$ is: