Question

question 11 at an animal rescue, 30% of the animals are dogs and 70% of the animals are cats. if the average age of the dogs is 8 months and the average age of the cats is 4 months, what is the average age of all the animals?

Explanation:

Step1: Use weighted - average formula

Let the proportion of dogs be $p_1 = 0.3$ and their average age $\bar{x}_1=8$ months, and the proportion of cats be $p_2 = 0.7$ and their average age $\bar{x}_2 = 4$ months. The formula for the weighted - average $\bar{x}=\sum_{i = 1}^{n}p_i\bar{x}_i$.

Step2: Calculate the weighted - average

$\bar{x}=p_1\bar{x}_1 + p_2\bar{x}_2=0.3\times8+0.7\times4$.
First, calculate $0.3\times8 = 2.4$ and $0.7\times4=2.8$.
Then, $\bar{x}=2.4 + 2.8=5.2$ months.

Answer:

$5.2$ months