Question

The average age of 20 boys is 15, and the average age of 15 girls is 13. What is the average age of all the boys and girls?

Answer 1

As per the question, we have:
Average age of $20$ boys = $15$ years
Average age of $15$ girls = $13$ years

The same data can be represented in table format as:

	Number of students	Average weight
Boys	20	15
Girls	15	13

$\therefore$ Average age
$=\frac{\text{(Number of boys}\times \text{Boys' average age)}+\text{(Number of girls}\times \text{Girls' average age)}}{\text{Number of boys + Number of girls}}$

$\underset{–}{\text{Note:}}$ Here, the weighted factors are the number of boys and the number of girls, whereas the data points are their average ages.

Consider,
$w_1=\text{Numebr of boys}=20$
$w_2=\text{Numebr of girls}=15$
$x_1=\text{Average age of boys}=15\text{years}$
$x_2=\text{Average age of girls}=13\text{years}$

$=\frac{(w_1\times x_1)+(w_2\times x_2)}{w_1+w_2}$

$=\frac{(20\times 15)+(15\times 13)}{20+15}$

$=\frac{300+195}{35}=14.14\text{years}$

$\therefore$ The average age of all the boys and girls is $14.14$ years.