The mean age of eight boys is 16 years. If two more boys, with ages 18 years and 14 years, join them, the resulting mean age is :

1. 18 years

2. 14 years

3. 16 years

4. 32 years

By formula,

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

Given,

The mean age of eight boys is 16 years.

$\therefore \text{Mean age} = \dfrac{\text{Total age}}{\text{No. of boys}} \\[1em] \Rightarrow 16 = \dfrac{\text{Total age}}{8} \\[1em] \Rightarrow \text{Total age} = 16 \times 8 \\[1em] \Rightarrow \text{Total age} = 128 \text{ years}.$

Given,

Two more boys with ages 18 years and 14 years join the group.

Total age now = 128 + 18 + 14 = 160.

New mean age = $\dfrac{\text{New total age}}{\text{No. of boys}} = \dfrac{160}{10}$ = 16 years.

Hence, Option 3 is the correct option.