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Mean Absolute Deviation (MAD) — Formula & Guide
MAD measures how spread out data values are from their mean. It tells you the average distance each data point is from the mean — in the same units as your data.
MAD = Σ|xᵢ − x̄| / n
where x̄ = mean, xᵢ = each value, n = number of values
|xᵢ − x̄| = absolute value of deviation (always positive)
where x̄ = mean, xᵢ = each value, n = number of values
|xᵢ − x̄| = absolute value of deviation (always positive)
MAD Step-by-Step Example
Data: {2, 4, 6, 8, 10}
- Step 1 — Mean: (2+4+6+8+10) ÷ 5 = 6
- Step 2 — Deviations: |2−6|=4, |4−6|=2, |6−6|=0, |8−6|=2, |10−6|=4
- Step 3 — Sum of deviations: 4+2+0+2+4 = 12
- Step 4 — MAD: 12 ÷ 5 = 2.4
MAD vs Standard Deviation
MAD = Σ|xᵢ − x̄| / n (uses absolute value)
SD = √[Σ(xᵢ − x̄)² / n] (uses squares)
SD = √[Σ(xᵢ − x̄)² / n] (uses squares)
MAD is simpler and more robust to outliers. Standard deviation gives more weight to extreme values. Both measure spread — MAD is preferred for beginners (6th–7th grade math).
MAD Practice Examples
{2, 4, 6, 8, 10} → Mean=6, MAD=2.4
{51, 38, 79, 46, 57} → Mean=54.2, MAD=11.04
{4, 8, 11, 19} → Mean=10.5, MAD=4.5
{10, 10, 10, 10} → Mean=10, MAD=0 (all same)
{51, 38, 79, 46, 57} → Mean=54.2, MAD=11.04
{4, 8, 11, 19} → Mean=10.5, MAD=4.5
{10, 10, 10, 10} → Mean=10, MAD=0 (all same)
When MAD = 0
If MAD = 0, all values in the dataset are identical — there is no variation at all. Example: {5, 5, 5, 5} → Mean=5, every deviation=0, MAD=0.
MAD in 6th and 7th Grade Math
MAD is a key concept in middle school statistics. Students learn to:
- Find the mean of a dataset
- Calculate deviations from the mean
- Use absolute values (no negative deviations)
- Average the deviations to get MAD
- Compare variability between two datasets using MAD
Related Calculators
Also check our Standard Deviation Calculator, Mean Median Mode Calculator, Integer Calculator, Prime Factorization Calculator, and all Math Calculators on CalcVelo.