First slide

Introduction to statistics

Question

$If the arithmetic mean of the numbers x_{1}, x_{2}, x_{3}, \dots, x_{n} is \bar{x}, then the arithmetic mean of the numbers a x_{1} + b, a x_{2} + b, a x_{3} + b, \dots, a x_{n} + b, where a, b are two constants, would be$

Easy

A

$x$
B

$n a x + n b$
C

$a x$
D

$a x + b$

Solution

Required Mean
$\begin{aligned} = \frac{(a x_{1} + b) + (a x_{2} + b) + \dots + (a x_{n} + b)}{n} \\ = \frac{a (x_{1} + x_{2} + \dots + x_{n})}{n} + b = a \bar{x} + b \\ (∵ \frac{x_{1} + x_{2} + \dots + x_{n}}{n} = \bar{x}) \end{aligned}$

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