Lesson 5: Mean Absolute Deviation

Property

The mean absolute deviation (MAD) is a measure of variability (or spread) of the data that uses each data value.
To compute the MAD, first find the mean of the data set, $\overline{x}$.
Then, find the absolute deviation of each data point from the mean: $|x - \overline{x}|$.
The mean absolute deviation is the mean of these absolute deviations for all the data points.

Examples

• For the data set {3, 5, 7, 9}, the mean is 6. The absolute deviations are $|3-6|=3$, $|5-6|=1$, $|7-6|=1$, and $|9-6|=3$. The MAD is $\frac{3+1+1+3}{4} = 2$.
• A cat's daily nap times in hours are 14, 15, 16, 15. The mean is 15 hours. The absolute deviations are $|14-15|=1$, $|15-15|=0$, $|16-15|=1$, and $|15-15|=0$. The MAD is $\frac{1+0+1+0}{4} = 0.5$ hours.
• Group A's scores {80, 85, 90} have a MAD of 3.33. Group B's scores {70, 85, 100} have a MAD of 10. Group B's scores have greater variability.

Explanation

The MAD tells you the average distance of each data point from the mean. A larger MAD indicates that the data values are more spread out, while a smaller MAD means the data points are clustered closely around the mean.

Property

The Mean Absolute Deviation (MAD) provides a measure of how spread out data points are from the mean.
A larger MAD indicates greater variability, while a smaller MAD indicates data points are clustered closer to the mean.
MAD values should be interpreted in the context of the data and compared to the mean to understand the relative spread.

Examples