The mean of 15 numbers is 27. If each number is multiplied by 4, what will be the mean of the new numbers?
Let the numbers be x1, x2,...x15
We know:
Mean $=\frac{\text { Sum of observa tions }}{\text { Number of observations }}$
Thus, we have:
$27=\frac{x_{1}+x_{2}+\ldots \ldots \ldots+x_{15}}{15}$
$\Rightarrow x_{1}+x_{2}+\ldots \ldots \ldots+x_{15}=405 \ldots \ldots \ldots$ (i)
After multiplication, the numbers become $4 x_{1}, 4 x_{2}, \ldots 4 x_{15}$
$\therefore$ New Mean $=\frac{4 x_{1}+4 x_{2}+\ldots \ldots+4 x_{15}}{15}$
$=\frac{4\left(x_{1}+x_{2}+\ldots \ldots+x_{15}\right)}{15}$
$=\frac{4 \times 405}{15} \quad[$ From $(\mathrm{i})]$
$=\frac{1620}{15}$
$=108$
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