If the mean of x₁ and x₂ is 12.5 and mean of x₁, x₂ and x₃ is 16. The value of x₃ is :

1. 32

2. 3.5

3. 285

4. 23

Given:

The mean of x₁ and x₂ = 12.5

Mean = $\dfrac{\text{Sum of all observations }}{\text{Number of all observations }}$

⇒ 12.5 = $\dfrac{x$1 + x2}{2}

⇒ 12.5 x 2 = ${x$1 + x2}

⇒ ${x$1 + x2} = 25 ……………(1)

The mean of x₁, x₂ and x₃ = 16

⇒ 16 = $\dfrac{x$1 + x2 + x_3}{3}

⇒ 16 x 3 = ${x$1 + x2 + x_3}

⇒ ${x$1 + x2 + x_3} = 48 ……………(2)

Subtracting equation (1) from (2), we get

⇒ ${(x$1 + x2 + x3) - (x1 + x_2)} = 48 - 25

⇒ ${x_3}$ = 23

Hence, option 4 is the correct option.