Mean Absolute Deviation (MAD) Calculator

Provide a comma-separated list of numbers to calculate the MAD.

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.


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