In the usual notations,$Z - M = \ldots \ldots \ldots \quad (M - \bar{x})$

$Z - \bar{x} = \dots \times (M - \bar{x})$

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

For some given data,if $Z + M = 108$ and $Z - M = -6$,then the mean $\bar{x} = \ldots \ldots \ldots$

The marks distribution of $30$ students in a mathematics examination is given in the table. Find the mode of this data. Also,compare and interpret the mode and the mean.

Class interval	$10-25$	$25-40$	$40-55$	$55-70$	$70-85$	$85-100$
Number of students	$2$	$3$	$7$	$6$	$6$	$6$

$100$ surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:

Number of letters	$1-4$	$4-7$	$7-10$	$10-13$	$13-16$	$16-19$
Number of surnames	$6$	$30$	$40$	$16$	$4$	$4$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also,find the modal size of the surnames.