How to Calculate Mean Absolute Deviation (MAD)

How to Calculate Mean Absolute Deviation (MAD)

Mean Absolute Deviation (MAD) measures the average distance each data point falls from the mean. Unlike variance or standard deviation, MAD uses absolute values rather than squaring, making it more intuitive and less sensitive to outliers.

The Formula

MAD = (1/n) × Σ|xᵢ − x̄|

Where:

• n = number of data points
• xᵢ = each individual value
• x̄ = the mean of all values
• |...| = absolute value

Step-by-Step Example

Data set: 9

Step 1: Calculate the mean. x̄ = (4 + 7 + 13 + 2 + 1 + 9) / 6 = 36 / 6 = 6

Step 2: Find the absolute deviation of each point from the mean. |4 − 6| = 2 |7 − 6| = 1 |13 − 6| = 7 |2 − 6| = 4 |1 − 6| = 5 |9 − 6| = 3

Step 3: Calculate the mean of these absolute deviations. MAD = (2 + 1 + 7 + 4 + 5 + 3) / 6 = 22 / 6 = 3.67

Interpreting MAD

A MAD of 3.67 means that on average, each value in the dataset is about 3.67 units away from the mean. A smaller MAD indicates the data is tightly clustered; a larger MAD indicates more spread.

MAD vs. Standard Deviation

Use our MAD calculator for any dataset.