Statistics

Mean Absolute Deviation Calculator

Find the average absolute distance from the mean.

Value 1

Value 2

Value 3

Value 4

Value 5

Calculated Output

Mean absolute deviation 5.76

Mean 13.2

Formula: MAD = Σ|xᵢ − mean| ÷ n

Step-by-Step Breakdown

1. ▶ Data: 4, 8, 15, 16, 23 (n = 5)

2. ▶ Step 1 — Mean (μ):

3. μ = (4 + 8 + 15 + 16 + 23) ÷ 5 = 66 ÷ 5 = 13.2

4. ▶ Step 2 — Absolute Deviations |xᵢ − μ|:

5. |x1 − μ| = |4 − 13.2| = 9.2

6. |x2 − μ| = |8 − 13.2| = 5.2

7. |x3 − μ| = |15 − 13.2| = 1.8

8. |x4 − μ| = |16 − 13.2| = 2.8

9. |x5 − μ| = |23 − 13.2| = 9.8

10.

11. ▶ Step 3 — Sum of Absolute Deviations Σ|xᵢ − μ|:

12. 9.2 + 5.2 + 1.8 + 2.8 + 9.8 = 28.8

13. ▶ Step 4 — Mean Absolute Deviation (MAD):

14. MAD = Σ|xᵢ − μ| ÷ n

15. MAD = 28.8 ÷ 5 = 5.76

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The math behind it

MAD = average of |value − mean|.

4,8,15,16,23 → mean 13.2, MAD 6.16.

Vs standard deviation?

MAD uses absolute values; SD squares them (weighting outliers more).