If the mean of the first $n$ natural numbers is equal to $\frac{n + 7}{3}$,then what is the value of $n$?

The arithmetic mean of the first $n$ natural numbers is:

The mean of a set of numbers is $\bar{x}$. If each number is multiplied by $\lambda$,then the mean of the new set is

If $\mu$ is the mean of a distribution $(y_i, f_i)$,then $\sum f_i(y_i - \mu) = $

Find the median of the following frequency distribution.

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
$f_i$	$8$	$30$	$40$	$12$	$10$

The number of observations in a group is $40$. If the average of the first $10$ observations is $4.5$ and the average of the remaining $30$ observations is $3.5$,then the average of the whole group is: