To find the mean absolute deviation (MAD), you need to calculate the average distance between each data point and the mean of the dataset. Here's a step-by-step process:
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Calculate the Mean: First, determine the arithmetic mean (average) of your dataset. You do this by adding up all the values and dividing by the total number of values.
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Find the Absolute Deviations: For each number in the dataset:
- Subtract the mean you calculated in step one.
- Take the absolute value of the result. This will make all the deviations positive.
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Sum the Absolute Deviations: Add up all the absolute deviations you calculated in the previous step.
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Calculate the Mean Absolute Deviation: Divide the sum of the absolute deviations by the total number of values in your dataset. According to our reference, the mean absolute deviation is calculated by "dividing the sum above by the total number of values in the data set."
Here's a table that summarizes the process:
| Step | Action | Formula |
|---|---|---|
| 1 | Calculate the mean of the dataset | Mean = (Sum of Values) / (Number of Values) |
| 2 | Find the absolute value of the difference between each value and the mean | |
| 3 | Sum all the absolute deviations | Sum of Absolute Deviations |
| 4 | Divide the sum by the number of data points | MAD = (Sum of Absolute Deviations) / (Number of Values) |
Example
Let's say you have the following dataset: 4, 7, 10, 13, 16
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Mean: (4 + 7 + 10 + 13 + 16) / 5 = 50 / 5 = 10
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Absolute Deviations:
- |4 - 10| = 6
- |7 - 10| = 3
- |10 - 10| = 0
- |13 - 10| = 3
- |16 - 10| = 6
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Sum of Absolute Deviations: 6 + 3 + 0 + 3 + 6 = 18
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Mean Absolute Deviation: 18 / 5 = 3.6
Therefore, the mean absolute deviation of the dataset is 3.6.
The mean absolute deviation is a useful measure of how spread out the data points are around the mean. A larger MAD indicates more variability in the dataset.
