Question

the weights of six animals at the zoo are shown in the table below.
weights of animals
(pounds)
5
24
38
52
66
85
what is the mean absolute deviation? round to the nearest tenth.

Explanation:

Step1: Calculate the mean

First, find the sum of the weights: \(5 + 24 + 38 + 52 + 66 + 85 = 270\)
Then, divide by the number of animals (6) to get the mean: \(\frac{270}{6} = 45\)

Step2: Find the absolute deviations

Calculate the absolute difference between each weight and the mean:

• \(|5 - 45| = 40\)
• \(|24 - 45| = 21\)
• \(|38 - 45| = 7\)
• \(|52 - 45| = 7\)
• \(|66 - 45| = 21\)
• \(|85 - 45| = 40\)

Step3: Calculate the mean of these absolute deviations

Sum the absolute deviations: \(40 + 21 + 7 + 7 + 21 + 40 = 136\)
Divide by the number of animals (6): \(\frac{136}{6} \approx 22.7\) (rounded to the nearest tenth)

Answer:

22.7