The mean absolute deviation (MAD) in math is the average of the absolute differences between each data point in a set and the mean (average) of that data set. It measures the average "distance" data points are from the center.
Understanding Mean Absolute Deviation
MAD provides a measure of the variability or spread in a dataset. Unlike standard deviation, which squares the differences, MAD uses absolute values. This makes it less sensitive to extreme values (outliers) but still provides valuable insight into the data's dispersion.
Calculating the Mean Absolute Deviation
Here's how to calculate the mean absolute deviation:
- Calculate the Mean: Find the average of all the data points in the dataset.
- Calculate the Absolute Deviations: For each data point, subtract the mean and take the absolute value of the result. This gives you the distance of each point from the mean, ignoring whether it's above or below.
- Calculate the Mean of the Absolute Deviations: Find the average of all the absolute deviations you calculated in step 2. This is the mean absolute deviation.
Example
Let's say we have the following dataset: 2, 4, 6, 8, 10
- Mean: (2 + 4 + 6 + 8 + 10) / 5 = 6
- Absolute Deviations:
- |2 - 6| = 4
- |4 - 6| = 2
- |6 - 6| = 0
- |8 - 6| = 2
- |10 - 6| = 4
- Mean Absolute Deviation: (4 + 2 + 0 + 2 + 4) / 5 = 2.4
Therefore, the mean absolute deviation of this dataset is 2.4. This means that, on average, each data point is 2.4 units away from the mean of 6.
Why Use Mean Absolute Deviation?
- Simplicity: It is easier to calculate and understand compared to standard deviation.
- Robustness: Less sensitive to outliers than standard deviation because it uses absolute values instead of squared values.
- Interpretability: Provides a direct measure of the average distance from the mean, making it easy to interpret.
Limitations
- Less commonly used in advanced statistical analyses compared to standard deviation.
- Mathematically less tractable than standard deviation.
In summary, the mean absolute deviation is a simple and intuitive way to measure the spread or variability within a dataset by calculating the average distance of each data point from the mean.
