Question

The mean weight of 8 numbers is 15 kg. If each number is multiplied by 2, what will be the new mean?

Answer 1

Let x₁, x₂, x₃...x₈ be the eight numbers whose mean is 15 kg. Then,

$15=\frac{x_1+x_2+x_3+...+x_8}{8}$

x₁ + x₂ + x₃ +...+ x₈ = 15×8
⇒x₁ + x₂ + x₃ +...+ x₈ = 120.

Let the new numbers be 2x₁ , 2x₂, 2x₃, ...2x_8. Let M be the arithmetic mean of the new numbers.
Then,

​$$\begin{gathered} M=\frac{2x_1+2x_2+2x_3+....+2x_8}{8} \\ =>M=\frac{2(x_1+x_2+x_3+....x_8)}{8}=>M=\frac{2\times 120}{8}=>M=30 \end{gathered}$$