The arithmetic mean of the first $n$ natural numbers 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	$2$	$4$	$5$	$8$	$7$	$3$	$2$

If $\bar{X}_1$ and $\bar{X}_2$ are the means of two series such that $\bar{X}_1 < \bar{X}_2$,and $\bar{X}$ is the combined mean of the two series,then which of the following is true?

If the mean of the numbers $27 + x$,$31 + x$,$89 + x$,$107 + x$,and $156 + x$ is $82$,then the mean of $130 + x$,$126 + x$,$68 + x$,$50 + x$,and $1 + x$ is:

The $A.M.$ of a $50$ set of numbers is $38$. If two numbers of the set,namely $55$ and $45$,are discarded,the $A.M.$ of the remaining set of numbers is

The observations $29, 32, 48, 50, x, x + 2, 72, 78, 84, 95$ are arranged in ascending order. If their median is $63$,what is the value of $x$?