Question

If the arithmetic mean of the number $x_1,x_2,x_3.........,x_n$ is $\overline{x}$ , then the arithmetic mean of numbers$a{x}_1,+b,a{x}_2+b,a{x}_3+b,.............a{x}_n+b,$
where a, b are two constants would be

• A. $\overline{x}$
• B. $na\overline{x}+nb$
• C. $a\overline{x}$
• D. $a\overline{x}+b$

Answer 1

The correct option is D $a\overline{x}+b$

$Requiredmean=\frac{(a{x}_1+b)+(a{x}_2+b)+....+(a{x}_n+b)}{n}$
$=\frac{a(x_1+x_2+....+x_n)+nb}{n}=\overline{ax}+b,$
$(\therefore \frac{x_1+x_2+...+xn}{n}=\overline{x}).$