Question

The mean of $16$ numbers is $54$. If each number is divided by $9$ what will be the new mean?

Answer 1

Let $a_1,a_2,....,a_{16}$ be $16$ numbers.

Mean $=\frac{a_1+a_2+....+a_{16}}{16}=54$

$\therefore a_1+a_2+....+a_{16}=54\times 16$

New mwan $=\frac{\frac{a_1}{9}+\frac{a_2}{9}+....+\frac{a_{16}}{9}}{16}$

$=\frac{1}{9}\times \left(\frac{a_1+a_2+....+a_{16}}{16}\right)$

$=\frac{1}{9}\times 54=6$

New Mean $=6$