Question

What is the mean absolute deviation (MAD) of the data set? Round your answer to the nearest tenth, if necessary. {9.1, 9.3, 9.1, 9.5, 9.8, 9.9}

Answer 1

The mean absolute deviation of the data set is
`MAD \approx 0.3`

Explanation:

The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset.

To find the mean absolute deviation you must:

1. Calculate the mean

Found by adding all data points and dividing by the number of data points.

`\mu=(9.1+9.3+9.1+9.5+9.8+9.9)/(6) \\\\\mu = (56.7)/(6)\\\\\mu=9.45`

2. Calculate how far away each data point is from the mean using positive distances. These are called absolute deviations.

`\begin{array}{cc}Data \:point&Distance \:from \:mean\\9.1&|9.1-9.45|=0.35\\9.3&|9.3-9.45|=0.15\\9.1&|9.1-9.45|=0.35\\9.5&|9.5-9.45|=0.05\\9.8&|9.8-9.45|=0.35\\9.9&|9.9-9.45|=0.45\end{array}`

3. Add those deviations together.

`0.35+0.15+0.35+0.05+0.35+0.45=1.7`

4. Divide the sum by the number of data points.

`MAD=(1.7)/(6) \approx 0.28333\approx 0.3`