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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 ______.
Options
18 years
14 years
16 years
32 years
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Solution
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.
\[\text{New mean age} = \frac{\text{New total age}}{\text{No. of boys}} = \frac{160}{10} = 16\ \text{years}.\]
