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

For a symmetrical distribution,if ${Q_1} = 25$ and ${Q_3} = 45$,the median is

The upper quartile for the following distribution is given by the size of:

Size of Item	$1$	$2$	$3$	$4$	$5$	$6$	$7$
Frequency	$2$	$4$	$5$	$8$	$7$	$3$	$2$

The median of a set of $13$ observations which are in decreasing order is $18.6$. If the first two observations are increased by $1$ and the last three observations are decreased by $5$,then the median of the set of new observations is-

The arithmetic mean of the following discrete data $12, 14, 20, 23, 25, 32$ is given by

Find the mean of the following frequency distribution:

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$
$f_i$	$12$	$18$	$27$	$20$	$17$	$6$