First slide

Introduction to statistics

Question

${If the arithmetic mean of the numbers x}_{1}, x_{2}, x_{3}, \dots, x_{k} i s \bar{x}, t h e n t h e a r i t h m e t i c m e a n o f t h e n u m b e r s$
$a x_{1} + b, a x_{2} + b, a x_{3} + b . . . . . . . . . . a x_{n} + b,$
$w h e r e a, b a r e t w o c o n s t a n t s, w o u l d b e$

Easy

A

$x$
B

$n a x + n b$
C

$a x$
D

$a x + b$

Solution

$Required mean is \frac{(a x_{1} + b) + (a x_{2} + b) + \dots + (a x_{n} + b)}{n}$
$\begin{array}{l} = \frac{a (x_{1} + x_{2} + \dots + x_{n})}{n} + b = a \bar{x} + b \\ (∵ \frac{x_{1} + x_{2} + \dots + x_{n}}{n} = \bar{x}) \end{array}$

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