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Byju's Answer

Standard VIII

Mathematics

Solving Equations with Linear Expressions on One Side and Numbers on the Other Side

If x is the a...

Question

If x is the arithmetic mean of n observations $x_{1} + x_{2}, . . . . . . . . . . x_{n},$ then find the arithmetic mean of $x + a_{1} + x_{2} + a, . . . . . . . . . . x_{n} + a .$

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Solution

Given $x =$ Mean of $x_{1} + x_{2} + x_{3} + . . . . . . + x_{n}$
arithmetic mean $x = \frac{x_{1} + x_{2} + x_{3} + . . . . . . . . . + x_{n}}{n}$
Arithmetic mean of $x_{1} + a + x_{2} + a + . . . . . + x_{n} + a$
$= \frac{x_{1} + a + x_{2} + x + . . . . . . . + x_{n} + a}{n}$
$= \frac{(x_{1} + x_{2} + . . . . . . + x_{n}) + (a + . . . . . . n t e r m s)}{n}$
$= x + \frac{a (n)}{n}$
$= x + a$

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