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Mean Deviation Formula

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Chesser Ai Answer

MAD about the mean: MAD = (1/n) ∑_{i=1}^{n} |x_i – bar{x}|.

Key Concepts

  • Concept: Mean absolute deviation (MAD)
  • Concept: Central value: mean or median
  • Concept: Interpretation: average distance from center

Steps

  1. Action: Compute the mean bar{x}.
  2. Action: Compute |x_i – bar{x}| for each i.
  3. Action: Sum deviations and divide by n.

Formula

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

$$bar{x} = frac{1}{n} sum_{i=1}^{n} x_i$$

$$text{MAD}_{text{median}} = frac{1}{n} sum_{i=1}^{n} left| x_i – m right| quad text{(m = median)}$$

$$text{MAD}_{text{grouped}} = frac{1}{N} sum_{i} f_i left| c_i – bar{x} right| quad text{(N = total frequency)}$$

Example: Data {2, 4, 6, 8, 10}: mean = 6; MAD = (|4|+|2|+|0|+|2|+|4|)/5 = 12/5 = 2.4.

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