Cumulative frequency curve is also known as ........

In calculating the mean of grouped data,grouped in classes of equal width,we may use the formula $\bar{x} = a + \frac{\sum f_i d_i}{\sum f_i}$,where $a$ is the assumed mean. $a$ must be one of the mid-points of the classes. Is the last statement correct? Justify your answer.

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

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

Given below is a cumulative frequency distribution showing the marks secured by $50$ students of a class:

Marks	Below $20$	Below $40$	Below $60$	Below $80$	Below $100$
Number of students	$17$	$22$	$29$	$37$	$50$

Form the frequency distribution table for the data.

The mean of $15$ observations is $16$. If $2$ is added to each observation and then each result is divided by $3$,the new mean is:

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