If $\bar{x} = Z - 3$ and $M = 22$,then the mean is ..........

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.

Number of students per teacher	Number of states/$U$.$T$.
$15-20$	$3$
$20-25$	$8$
$25-30$	$9$
$30-35$	$10$
$35-40$	$3$
$40-45$	$0$
$45-50$	$0$
$50-55$	$2$

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

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$5$	$27$	$58$	$20$	$10$

For some given data,if $Z = 16$ and $M = 18$,then $\bar{x} = \ldots \ldots \ldots$

If $M = 72$ and $\bar{x} = 70$,then $Z = \ldots \ldots \ldots \ldots$

The mean and median of a frequency distribution are $72.5$ and $73.9$ respectively. Then,the mode of the data is $\ldots \ldots \ldots . . .$