Question

In a group, the ages (in years) of $8$ friends are $25,27,25,27,26,25,27,26$. The average age of the group is .

Answer 1

The given data set for the ages (in years) of $8$ friends are $\{25,27,25,27,26,25,27,26\}$.

The data set can be represented using frequency table as

Age (in years)	Frequency
$25\left(n_1\right)$	$3\left(w_1\right)$
$26\left(n_2\right)$	$2\left(w_2\right)$
$27\left(n_3\right)$	$3\left(w_3\right)$

In the above frequency table, the number of friends $(3,2,3)$ having a particular age denote the weighted factors $(w_1,w_2,w_3)$, whereas the corresponding ages $(25,26,27)$ denote the data points $(n_1,n_2,n_3)$.

$\therefore$ Average age of $8$ friends

$=\frac{(w_1\times n_1)+(w_2\times n_2)+(w_3\times n_3)}{w_1+w_2+w_3}$

$=\frac{(3\times 25)+(2\times 26)+(3\times 27)}{3+2+3}$

$=\frac{208}{8}=26$ years

$\therefore$ The average age of the group of $8$ friends is $26$ years.