Mean Absolute Deviation (MAD) Calculator
Our mean absolute deviation calculator accurately measures the average distance between each data point and the central tendency.
Consider student test scores: 85, 92, 78, 88, 95
Calculate mean: (85 + 92 + 78 + 88 + 95) ÷ 5 = 87.6
Find absolute deviations: |85-87.6|, |92-87.6|, |78-87.6|, |88-87.6|, |95-87.6|
Calculate MAD: (2.6 + 4.4 + 9.6 + 0.4 + 7.4) ÷ 5 = 4.88
MAD Calculation Formula
The core formula for calculating Mean Absolute Deviation is:
MAD = Σ|x - μ| ÷ n
Where:
- x represents individual values
- μ signifies the arithmetic mean
- n denotes total observations
- |x – μ| indicates absolute differences
How to Calculate Mean Absolute Deviation
Step 1: Calculate the Mean (Average)
- Formula: Mean = (Sum of all values) ÷ (Number of values)
- Example: For dataset [6, 8, 4, 10, 2, 8, 6]
- Calculation: (6 + 8 + 4 + 10 + 2 + 8 + 6) ÷ 7 = 44 ÷ 7 = 6.29
Step 2: Calculate Absolute Deviations
For each number:
- 6: |6 – 6.29| = 0.29
- 8: |8 – 6.29| = 1.71
- 4: |4 – 6.29| = 2.29
- 10: |10 – 6.29| = 3.71
- 2: |2 – 6.29| = 4.29
- 8: |8 – 6.29| = 1.71
- 6: |6 – 6.29| = 0.29
Step 3: Calculate Final MAD
- Add all absolute deviations: (0.29 + 1.71 + 2.29 + 3.71 + 4.29 + 1.71 + 0.29)
- Divide by number of values (7)
- Final MAD = 14.29 ÷ 7 = 2.04
Examples
Dataset 1: 6, 2, 8, 4, 8, 6, 8, 8
Mean = 6.25 MAD = 2 (average absolute deviation)
Dataset 2: 10, 4, 12, 4, 2, 10, 10, 6
Mean = 7.25 MAD = 3.5
Dataset 3: 10, 15, 18, 8, 4
Mean = 11 MAD = 4.8
Dataset 4: 4, 2, 2, 3, 5, 4, 2, 1, 5, 2
Mean = 3 MAD = 1.2
Dataset 5: 5, 9, 1, 5, 2, 5, 5, 5, 9, 3
Mean = 4.9 MAD = 2.26
Dataset 6: 10, 2, 6, 12, 6, 10, 4, 12
Mean = 7.75 MAD = 3.5
Dataset 7: 8, 4, 8, 8, 10, 2, 4, 4
Mean = 6 MAD = 2.5
Dataset 8: 2, 8, 6, 8, 6, 8, 10, 12
Mean = 7.5 MAD = 2.5
What is Mean Absolute Deviation?
Mean Absolute Deviation (MAD) is a statistical measurement that quantifies variability within a dataset by calculating the average distance between each data point and the mean. This robust metric helps researchers and analysts understand how spread out numbers are in a dataset.