Question

Let $\overline{x}$ be the mean of $x_1,x_2,x_3...x_n$. If $x_i=a+c{y}_i$ for some constants $a$ and $c$, then what will be the mean of $y_1,y_2,y_3....y_n$?

• A. $a+c\overline{x}$
• B. $a-\frac{1}{c}\overline{x}$
• C. $\frac{1}{c}\overline{x}-a$
• D. $\frac{\overline{x}-a}{c}$

Answer 1

The correct option is D $\frac{\overline{x}-a}{c}$

Let Mean of $x_i=\overline{x}$

$\Rightarrow$ Mean of $a+c{y}_i=\overline{x}$

$\Rightarrow$ Mean of $c{y}_i=\overline{x}-a$

$\Rightarrow$ Mean of $y_i=\frac{\overline{x}-a}{c}$