Mean Deviation About Mean Formula

Mean deviation about the mean = (1/n) Σ|x_i − x̄|.

Key Concepts

• Concept: Definition of mean deviation
• Concept: Use of the sample mean overline{x}
• Concept: Population vs. sample versions

Steps

1. Action: Compute the mean overline{x}
2. Action: Find absolute deviations |x_i − overline{x}|
3. Action: Average deviations: (1/n) ∑ |x_i − overline{x}|

Formula

$$overline{D} = frac{1}{n} sum_{i=1}^{n} left| x_i – overline{x} right|$$

For grouped data: $$overline{D} = frac{1}{N} sum_{i} f_i left| x_i – overline{x} right|$$

Notes

• Population vs sample: Use μ or x̄ accordingly; replace n with N for populations.
• Interpretation: MAD around the mean measures typical absolute deviation from the mean.
• Relation to normal distribution: For a normal distribution, MAD about the mean ≈ σ√(2/π) ≈ 0.798σ.