Question

The mean of 75 numbers is 35. If each number is multiplied by 4, find the new mean.

Answer 1

Let x₁, x₂, x₃, ... x₇₅ be 75 numbers with their mean equal to 35. Then,

$\Rightarrow 35=\frac{x_1+x_2+x_3+...+x_{75}}{75}$

x₁+ x₂ + x₃ +... + x₇₅ = 35 ×75

⇒ x₁ + x₂ + x₃ +... + x₇₅ = 2625

The new numbers are 4x₁, 4x₂, 4x₃, ...4x_75. Let M be the arithmetic mean of the new numbers. Then,

$$\begin{gathered} \Rightarrow M=\frac{4x_1+4x_2+4x_3+...+4x_{75}}{75} \\ \Rightarrow M=\frac{4(x_1+x_2+x_3+...+x_{75})}{75} \\ \Rightarrow M=\frac{4\times 2625}{75}\Rightarrow M=35\times 4\Rightarrow M=140. \end{gathered}$$