If the mean of x₁, x₂ is 7.5, and the mean of x₁, x₂, x₃ is 8, then the value of x₃ is

1. 9

2. 8

3. 7.5

4. 6

By formula,

$\text{Mean} = \dfrac{\text{Sum of observations}}{\text{No. of observations}}$

Given, Mean of x₁, x₂ = 7.5

$\therefore 7.5 = \dfrac{x$1 + x2}{2} \\[1em] \Rightarrow x1 + x2 = 15 ………..(i)

Given, Mean of x₁, x₂ and x₃ = 8

$\therefore 8 = \dfrac{x$1 + x2 + x3}{3} \\[1em] \Rightarrow x1 + x2 + x3 = 24 ………..(ii)

Subtracting equation (i) from (ii), we get :

⇒ x₁ + x₂ + x₃ - (x₁ + x₂) = 24 - 15

⇒ x₁ - x₁ + x₂ - x₂ + x₃ = 9

⇒ x₃ = 9.

Hence, Option 1 is the correct option.