Question

the data below show the numbers of miles driven to work each day by the employees of a small company. 15, 25, 13, 15, 18, 20, 22, 24. the mean of the data is 19 miles. what is the mean absolute deviation of the data? 0 3.75 0.125 1.6

Explanation:

Step1: Calculate the absolute deviations

Find the absolute difference between each data - point and the mean.
For \(15\): \(|15 - 19|=4\)
For \(25\): \(|25 - 19| = 6\)
For \(13\): \(|13 - 19|=6\)
For \(15\): \(|15 - 19| = 4\)
For \(18\): \(|18 - 19|=1\)
For \(20\): \(|20 - 19| = 1\)
For \(22\): \(|22 - 19|=3\)
For \(24\): \(|24 - 19| = 5\)

Step2: Calculate the sum of absolute deviations

\(4 + 6+6 + 4+1+1+3+5=30\)

Step3: Calculate the mean absolute deviation

The number of data - points \(n = 8\). The mean absolute deviation (MAD) is \(\frac{30}{8}=3.75\)

Answer:

3.75