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Mean Deviation Formula

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Chesser Ai Answer

Mean deviation equals the average absolute deviation from the center.

Key Concepts

  • Concept: Mean absolute deviation
  • Concept: Center: mean μ or x̄
  • Concept: Absolute deviations: |x_i − center|

Steps

  1. Action: Choose center (mean μ or x̄)
  2. Action: Compute |x_i − center| for all i
  3. Action: Average: MD = (1/n) Σ |x_i − center|

Formula

$$text{MAD} = frac{1}{n} sum_{i=1}^{n} left| x_i – bar{x} right|$$

Population version: $$text{MAD}_{pop} = frac{1}{N} sum_{i=1}^{N} left| x_i – mu right|$$

General center a: $$text{MAD}(a) = frac{1}{n} sum_{i=1}^{n} left| x_i – a right|$$

Relation to normal distribution (optional): $$text{MAD} = sigma,sqrt{frac{2}{pi}} quad text{(for } X sim N(mu,sigma^2) text{)}$$

Example: For x = [2, 4, 6, 8], mean is 5; MAD = (|−3|+|−1|+|1|+|3|)/4 = 2.

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