If $¯ x$ is mean of $x_{1}, x_{2} . . . . . . . . . . x_{n},$ then prove that if a is added to each term then mean will be $(¯ x + a)$

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Solution

$\frac{x_{1}, x_{2} . . . . . . . . . . x_{n}}{n} = ¯ x$
If $a$ is added to each term, Let required no. is $A$ ,
then
$A = \frac{(x_{1} + a) + (x_{2} + a) + . . . . . . . . . . . . . . + (x_{n} + a)}{n}$
$= \frac{(x_{1} + x_{2} + . . . . . . . . . . . . . . + x_{n}) (a + a + . . . . . . n t i m e s)}{n}$
$= \frac{x_{1} + x_{2} + . . . . . . . . . . . . . . + x_{n}}{n} + \frac{n a}{n}$
$= ¯ x + a$

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