In a class, the average age of $20$ boys is $16$ years and the average age of $18$ girls is $15$ years. The average age of all the students is .

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Solution

The formula to calculate the weighted average is,

$Weighted Average = \frac{(w_{1} \times n_{1}) + (w_{2} \times n_{2}) + \dots + (w_{l} \times n_{l})}{w_{1} + w_{2} + \dots + w_{l}}$ ,

where $w_{1}, w_{2}, \dots w_{l}$ are the weighted factors and $n_{1}, n_{2}, \dots n_{l}$ are the data points.

The given data can be represented in tabular form as,

Here, $w_{1} = 20$ and $w_{2} = 18$ are the weighted factors and $n_{1} = 16$ and $n_{2} = 15$ are the corresponding data points.

Therefore, the weighted average age is calculated as,

$\begin{matrix} Weighted average age & = \frac{(20 \times 16) + (18 \times 15)}{20 + 15} = \frac{320 + 270}{38} = \frac{590}{38} = 15.52 \end{matrix}$

Hence, the average age of all the students is $15.52$ years.

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In a class, the average age of 20 boys is 16 years and the average age of 18 girls is 15 years. The average age of all the students is .

In a class, the average age of $20$ boys is $16$ years and the average age of $18$ girls is $15$ years. The average age of all the students is .