Question

The mean of $12$ numbers is $40$. If each number is divided by $8$ what will be the new mean of new numbers ?

Answer 1

Mean of $12$ numbers $=40$

Let The $12$ numbers be $x_1,x_2,x_3,.....,x_{12}$

$\frac{x_1,x_2,x_3,.....,x_{12}}{12}=40$

$\Rightarrow x_1,x_2,x_3,.....,x_{12}=40\times 12=480--\left(i\right)$

Now, when each number is divided by $8$ then new set of $12$ numbers is

$\frac{x_1}{8},\frac{x_2}{8},\frac{x_3}{8},.....,\frac{x_{12}}{8}$

So, new mean $=\frac{\frac{x_1}{8},\frac{x_2}{8},\frac{x_3}{8},.....,\frac{x_{12}}{8}}{12}=\frac{x_1,x_2,x_3,.....,x_{12}}{8\times 12}=\frac{480}{96}\left[usingi\right]$

Hence, new mean $=5$.