Definition: Mean absolute deviation, or MAD, is the average distance of the data values from their mean, and it measures how spread out the data are.
What is MAD?
MAD tells how far a typical data point sits from the mean. A small MAD means the data are tightly grouped.
How do you compute it?
- Find the mean.
- Find each value’s distance from the mean, ignoring sign.
- Average those distances.
For 4, 8, 9, 11, 13, the mean is 45 / 5 = 9. The distances are 5, 1, 0, 2, 4. Their sum is 12, and the MAD is 12 / 5 = 2.4.
How do you interpret it?
On average, the values are 2.4 units from the mean of 9. Compare with 6, 8, 9, 10, 12, which has the same mean but distances 3, 1, 0, 1, 3, so MAD = 8 / 5 = 1.6. That second set is less spread out.
What is the common error?
Skipping the absolute value. The signed differences always sum to 0, so you must use distances, not signed differences.
Example: Data 2, 6, 10 have mean 6 and MAD (4 + 0 + 4) / 3, about 2.67.