The mean of 12 numbers is 40. If each number is divided by 8, what will be the mean of the new numbers?
Let the numbers be x1, x2,...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) $]$
$=5$
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