Question

Mean of a certain number of observation is m If each observation is divided by x ($x\ne 0$) and increased by y then the mean of new observation is

• A. $mx+y$
• B. $\frac{mx+y}{x}$
• C. $\frac{m+xy}{x}$
• D. $m+xy$

Answer 1

The correct option is C $\frac{m+xy}{x}$

Let $x_1,x_2,x_3,...,x_n$be 'n' observations.
$\Rightarrow m=\frac{x_1+x_2+x_3+...+x_n}{n}$
Now , according to question, the observations becomes
$\frac{x_1}{x}+y,\frac{x_2}{x}+y,\frac{x_3}{x}+y,...,\frac{x_n}{x}+y$
Therefore, new mean is
$m^{\prime }=\frac{\frac{x_1}{x}+y+\frac{x_2}{x}+y+\frac{x_3}{x}+y+...+\frac{x_n}{x}+y}{n}$
$\Rightarrow m^{\prime }=\frac{\frac{1}{x}(x_1+x_2+x_3+...+x_n)+ny}{n}$
$\Rightarrow m^{\prime }=\frac{1}{x}\frac{x_1+x_2+x_3+...+x_n}{n}+y$
$\Rightarrow m^{\prime }=\frac{1}{x}\left(m\right)+y$
$\Rightarrow m^{\prime }=\frac{m+xy}{x}$
Option C is correct.