Question

Let $\stackrel{-}{x}$ be the mean of n observations $x_1,x_2,x_3,.....x_n$. If (a - b) is added to each observation, then what is the mean of the new set of observations?

• A. zero
• B. $\stackrel{-}{x}$
• C. $\stackrel{-}{x}-(a-b)$
• D. $\stackrel{-}{x}+(a-b)$

Answer 1

Answer: (D)

$\stackrel{-}{x}+(a-b)$

Given, $\frac{x_1+x_2+x_3+.....x_n}{n}=\stackrel{-}{x}$
$\therefore \frac{x_1+(a-b)+x_2+(a-b)+x_3+(a-b)+....+x_n+(a-b)}{n}$
$=\frac{x_1+x_2+x_3+.....x_n}{n}+\frac{n(a-b)}{n}$
$=\stackrel{-}{x}+(a-b)$