Question

The mean of a set of observations is $a$. If each observation is multiplied by $b$ and each product is decreased by $c$, then the mean of the new set of observations is

• A. $\frac{a}{b}+c$
• B. $ab-c$
• C. $\frac{a}{b}-c$
• D. $ab+c$

Answer 1

Answer: (B)

$ab-c$

Let $x_1,x_2,x_3,...,x_n$ be $n$ observations
Let $y_i=b{x}_i-c;i=1,2,...,n$. Then,
$\overline{Y}=b\overline{X}-c\Rightarrow \overline{Y}=ab-c$