For a given frequency distribution,$n=100, A=20$ and $\bar{x}=20$. Then,$\Sigma f_{i} d_{i}=\ldots \ldots \ldots . .$

The mean of ungrouped data and the mean calculated when the same data is grouped are always the same. Do you agree with this statement? Give reason for your answer.

In the formula $\bar{x} = A + \frac{\Sigma f_{i} u_{i}}{\Sigma f_{i}} \times c$ for the mean,$u_{i} = \ldots \ldots \ldots$

In a maths test taken by $35$ students,the average score of $15$ girls is $10$ and that of $20$ boys is also $10$. Which of the following can be calculated based on the data we have?

The mean of the following frequency distribution is $65$ and the total frequency is $100$. Find the missing frequencies $f_{1}$ and $f_{2}$.

Class	$15-35$	$35-55$	$55-75$	$75-95$	$95-115$
Frequency	$17$	$f_1$	$32$	$f_2$	$19$

The mean of $10$ observations is $15.7$. If a new observation $19$ is included,the new mean is ..........