Question

The mean of a set of observation is `overlinex`. If each observation is divided by α, α ≠ 0 and then is increased by 10, then the mean of the new set is ______.

Options

• `overlinex/α`

• `(overlinex + 10)/α`

• `(overlinex + 10α)/α`

• `αoverlinex + 10`

Answer 1

The mean of a set of observation is `overlinex`. If each observation is divided by α, α ≠ 0 and then is increased by 10, then the mean of the new set is `underlinebb((overlinex + 10α)/α)`.

Explanation:

Let x₁, x₂ ...., x_n be n observations.

Then, `overlinex = 1/n sumx_i` ;

Let y_i = `x_i/α + 10`

Then, `1/n sum_(i = 1)^n y_i = 1/α(1/n sum_(i = 1)^n x_i) + 1/n(10n)`

`\implies overliney = 1/α overlinex + 10 = (overlinex + 10α)/α`