Question

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 ______.

पर्याय

• 18 years

• 14 years

• 16 years

• 32 years

Answer 1

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 16 years.

Explanation:

By formula,

\[\text{Mean} = \frac{\text{Sum of observations}}{\text{No. of observations}}\]

Given,

The mean age of eight boys is 16 years.

\[\therefore \text{Mean age} = \frac{\text{Total age}}{\text{No. of boys}}\]

\[\Rightarrow 16 = \frac{\text{Total age}}{8}\]

⇒ Total age = 16 × 8

⇒ Total age = 128 years.

Given,

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

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

\[\text{New mean age} = \frac{\text{New total age}}{\text{No. of boys}} = \frac{160}{10} = 16\ \text{years}.\]