Understanding Mean Absolute Deviation (MAD)
MAD measures variability. It shows how far apart numbers are from their shared central balance point (the mean).
📍 Example 1: Small Integer Cluster
Data Set: 2, 4, 6, 8
- Find the Mean: (2 + 4 + 6 + 8) ÷ 4 = 5.
- Find absolute differences from 5: |2-5|=3, |4-5|=1, |6-5|=1, |8-5|=3.
- Average those differences: (3 + 1 + 1 + 3) ÷ 4 = 2.
MAD = 2 (On average, data points sit 2 units away from the mean)
📍 Example 2: Tight Cluster vs Spread
Data Set: 5, 5, 8, 10
- Find the Mean: (5 + 5 + 8 + 10) ÷ 4 = 7.
- Find absolute differences from 7: |5-7|=2, |5-7|=2, |8-7|=1, |10-7|=3.
- Average those differences: (2 + 2 + 1 + 3) ÷ 4 = 2.
MAD = 2 (Even with different data layout spacing, the average variation remains identical)