Question

The average age of $20$ cows is $6$ years and the average age of $15$ goats is $5$ years. What is the average age of these animals?

• A. $5.57\text{years}$
• B. $7.57\text{years}$
• C. $5\text{years}$

Answer 1

The correct option is A $5.57\text{years}$

As per the question,
$\bullet$ average age of $20$ cows= $6$ years
$\bullet$ average age of $15$ goats= $5$ years

The same data can be represented in table format as

Animal	Number	Average Age (in years)
Cow	$20$	$6$
Goat	$15$	$5$

$\therefore$ Average age of these animals

$=\frac{\text{(Number of cows}\times \text{Cow's average age)+(Number of goats}\times \text{Goat's average age)}}{\text{Number of cows+Number of goats}}$

$\underset{–}{\text{Note:}}$ Here, the weighted factors are number of cows and number of goats, whereas the data points are average age of cows and average age of goats.

Consider,
$w_1=\text{Numebr of cows}=20$
$w_2=\text{Numebr of goats}=15$
$x_1=\text{Average age of cows}=6\text{years}$
$x_2=\text{Average age of goats}=5\text{years}$

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

$=\frac{(20\times 6)+(15\times 5)}{20+15}$

$=\frac{195}{35}=5.57\text{years}$

$\therefore$ The average age of these animals is $5.57$ years.