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: \(5 + 24 + 38 + 52 + 66 + 85\).
\(5+24 = 29\), \(29+38 = 67\), \(67+52 = 119\), \(119+66 = 185\), \(185+85 = 270\).
The mean \(\bar{x}=\frac{270}{6}=45\).

Step2: Find absolute deviations

Calculate \(|x - \bar{x}|\) for each weight:

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

Step3: Calculate the mean of absolute deviations

Sum these absolute deviations: \(40 + 21 + 7 + 7 + 21 + 40\).
\(40+21 = 61\), \(61+7 = 68\), \(68+7 = 75\), \(75+21 = 96\), \(96+40 = 136\).
Mean absolute deviation (MAD) \(=\frac{136}{6}\approx22.7\) (rounded to the nearest tenth).

Answer:

\(22.7\)