Question

the following data points represent the yearly salaries of high school cheerleading coaches in dakota county (in thousands of dollars). 41, 38, 36, 57, 43 find the mean absolute deviation (mad) of the data set. thousand dollars show calculator

Explanation:

Step1: Calculate the mean of the data set.

The data set is \(41, 38, 36, 57, 43\). The formula for the mean \(\bar{x}\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n = 5\) and \(x_{i}\) are the data points.
\(\sum_{i=1}^{5}x_{i}=41 + 38+36 + 57+43=215\)
\(\bar{x}=\frac{215}{5} = 43\)

Step2: Find the absolute deviation of each data point from the mean.

For \(x_1 = 41\): \(|41 - 43|=2\)
For \(x_2 = 38\): \(|38 - 43| = 5\)
For \(x_3 = 36\): \(|36 - 43|=7\)
For \(x_4 = 57\): \(|57 - 43| = 14\)
For \(x_5 = 43\): \(|43 - 43|=0\)

Step3: Calculate the mean of these absolute deviations.

The sum of the absolute deviations is \(2 + 5+7 + 14+0=28\)
The mean absolute deviation (MAD) is \(\frac{28}{5}=5.6\)

Answer:

\(5.6\)