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The mean absolute deviation is a measure that describes the average absolute difference between the data points in a data set and the mean of the data set. It is calculated by finding the absolute difference between each data point and the mean, then taking the average of those absolute differences. Consider for example the following data set. 82, 85, 90, 75, 95, 85, 90, 70 The values are the scores of 8 students on a math test. The mean absolute deviation of the data set can be found by following these three steps.
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The mean of the data is 84.
| Data Value | Absolute Value of Difference |
|---|---|
| 82 | |82- 84| = 2 |
| 85 | |85- 84| = 1 |
| 90 | |90- 84| = 6 |
| 75 | |75- 84| = 9 |
| 95 | |95- 84| = 11 |
| 85 | |85- 84| = 1 |
| 90 | |90- 84| = 6 |
| 70 | |70- 84| = 14 |
The mean absolute deviation for the given data set is 6.25. This means that the average distance each data value is from the mean is 6.25 points. In other words, on average, the students' test scores deviate from the mean of 84 by 6.25 points.