Question

the weights, in pounds, of mikes five pet dogs are listed below. what is the mean absolute deviation (mad) of the weights? 16, 23, 27, 41, 53 type the answer in the box. pounds

Explanation:

Step1: Calculate the mean

First, find the mean (\(\mu\)) of the data set. The formula for the mean is \(\mu=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data points and \(n\) is the number of data points.
The data points are \(16,23,27,41,53\) and \(n = 5\).
\(\sum_{i=1}^{5}x_{i}=16 + 23+27 + 41+53=160\)
\(\mu=\frac{160}{5}=32\)

Step2: Find the absolute deviations

For each data point \(x_{i}\), calculate the absolute deviation \(|x_{i}-\mu|\):

• For \(x_{1}=16\): \(|16 - 32|=|- 16| = 16\)
• For \(x_{2}=23\): \(|23 - 32|=|-9| = 9\)
• For \(x_{3}=27\): \(|27 - 32|=|-5| = 5\)
• For \(x_{4}=41\): \(|41 - 32|=|9| = 9\)
• For \(x_{5}=53\): \(|53 - 32|=|21| = 21\)

Step3: Calculate the mean of absolute deviations

The formula for MAD is \(\text{MAD}=\frac{\sum_{i = 1}^{n}|x_{i}-\mu|}{n}\)
\(\sum_{i = 1}^{5}|x_{i}-\mu|=16 + 9+5 + 9+21=60\)
\(\text{MAD}=\frac{60}{5}=12\)

Answer:

12