If the arithmetic mean of the numbers x_1, x_ | vedclass

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(D) Given that the arithmetic mean of $x_1, x_2, ..., x_n$ is $\bar{x}$,we have $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$,which implies $\sum_{i=1}^{n}

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$a \bar{x} + b$

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(D) Given that the arithmetic mean of $x_1, x_2, ..., x_n$ is $\bar{x}$,we have $\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$,which implies $\sum_{i=1}^{n} x_i = n \bar{x}$.The required mean of the numbers $ax_1 + b, ax_2 + b, ..., ax_n + b$ is given by:$	ext{Mean} = \frac{(ax_1 + b) + (ax_2 + b) + ... + (ax_n + b)}{n}$$= \frac{a(x_1 + x_2 + ... + x_n) + nb}{n}$$= a \left( \frac{\sum_{i=1}^{n} x_i}{n} ight) + \frac{nb}{n}$$= a \bar{x} + b$

Marks obtained	No. of students
$0-10$	$2$
$10-20$	$18$
$20-30$	$30$
$30-40$	$45$
$40-50$	$35$
$50-60$	$20$
$60-70$	$6$
$70-80$	$3$

If the arithmetic mean of the numbers $x_1, x_2, x_3, ..., x_n$ is $\bar{x}$,then the arithmetic mean of the numbers $ax_1 + b, ax_2 + b, ax_3 + b, ..., ax_n + b$,where $a$ and $b$ are two constants,would be:

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Marks obtained No. of students

$0-10$ $2$

$10-20$ $18$

$20-30$ $30$

$30-40$ $45$

$40-50$ $35$

$50-60$ $20$

$60-70$ $6$

$70-80$ $3$

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 $x$?

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