Question

You breed poodles and notice there is bimodal distribution of poodle heights in your kennel. One group, with contains 24 dogs, averages 20.5 inches, another group that contains 12 dogs, averages 32.1 inches. What is the average height of the poodle in you kennel?

Answer 1

To determine the average height of the poodles in the kennel, a weighted average is calculated by multiplying each group's average height by its number of dogs, summing these products, and then dividing by the total number of dogs, resulting in an average height of approximately 24.37 inches.

Step-by-step explanation:

To find the average height of the poodles in the kennel, we need to calculate the weighted average of the two groups. This is done by multiplying the average height of each group by the number of dogs in that group, summing these products, and then dividing by the total number of dogs.

The calculation would look like this:

(Average height of group 1 × Number of dogs in group 1) + (Average height of group 2 × Number of dogs in group 2) ÷ Total number of dogs

(20.5 inches × 24 dogs) + (32.1 inches × 12 dogs) ÷ (24 dogs + 12 dogs) = (492 inches + 385.2 inches) ÷ 36 dogs = 877.2 inches ÷ 36 dogs = 24.3667 inches

So, the average height of a poodle in the kennel would be approximately 24.37 inches.