For some given data,if $M = 62.5$ and $\bar{x} = 64$,then $Z = \ldots$

Consider the data:

Class	$65-85$	$85-105$	$105-125$	$125-145$	$145-165$	$165-185$	$185-205$
Frequency	$4$	$5$	$13$	$20$	$14$	$7$	$4$

The difference between the upper limit of the median class and the lower limit of the modal class is:

The following table shows the ages of the patients admitted in a hospital during a year:

Age (in years)	$5$-$15$	$15$-$25$	$25$-$35$	$35$-$45$	$45$-$55$	$55$-$65$
Number of patients	$6$	$11$	$21$	$23$	$14$	$5$

Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

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 following frequency distribution gives the monthly consumption of electricity of $68$ consumers of a locality. Find the median,mean,and mode of the data and compare them.

Monthly consumption (in units)	Number of consumers
$65-85$	$4$
$85-105$	$5$
$105-125$	$13$
$125-145$	$20$
$145-165$	$14$
$165-185$	$8$
$185-205$	$4$

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