The mean of 12 numbers is 40. If each number is divided by 8,

Question:

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

 

Solution:

Let the numbers be x1x2,...x12.
We know:

Mean $=\frac{\text { Sum of observations }}{\text { Number of observations }}$

Thus, we have:

$40=\frac{x_{1}+x_{2}+\ldots+x_{12}}{12}$

$\Rightarrow x_{1}+x_{2}+\ldots+x_{12}=480 \quad \ldots \ldots(\mathrm{i})$

After division, the numbers become:

$\frac{x_{1}}{8}, \frac{x_{2}}{8}, \ldots, \frac{x_{12}}{8}$

$\therefore$ New mean $=\frac{\left(x_{1} / 8\right)+\left(x_{2} / 8\right)+\ldots .+(\sqrt{12} / 8)}{12}$

$=\frac{x_{1}+x_{2}+\ldots+x_{12}}{12 \times 8}$

$=\frac{x_{1}+x_{2}+\ldots+x_{12}}{96}$

$=\frac{480}{96} \quad[$ From (i) $]$

$=5$

 

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now