Mean Absolute Deviation Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Compare MAD and standard deviation for the data {1,5,5,5,9}\{1, 5, 5, 5, 9\}. Calculate both and explain when MAD is preferred.

Solution

  1. 1
    Mean: xห‰=25/5=5\bar{x} = 25/5 = 5
  2. 2
    MAD: absolute deviations are 4,0,0,0,44, 0, 0, 0, 4; MAD=8/5=1.6MAD = 8/5 = 1.6
  3. 3
    Variance: squared deviations 16,0,0,0,1616, 0, 0, 0, 16; ฯƒ2=32/5=6.4\sigma^2 = 32/5 = 6.4; ฯƒ=6.4โ‰ˆ2.53\sigma = \sqrt{6.4} \approx 2.53
  4. 4
    When MAD preferred: more interpretable (same units as data); less sensitive to outliers; useful for non-normal distributions; SD preferred for statistical inference (mathematically convenient)

Answer

MAD = 1.6; SD โ‰ˆ 2.53. MAD is more interpretable and outlier-resistant; SD is used for inference.
MAD and SD both measure spread but differ in sensitivity and interpretability. MAD is in original units and robust to outliers. SD is squared-based and used in virtually all statistical inference (because variance has nicer mathematical properties).

About Mean Absolute Deviation

The average distance between each data value and the mean of the data set. Calculated by finding the mean, computing the absolute value of each deviation from the mean, and averaging those absolute deviations.

Learn more about Mean Absolute Deviation โ†’

More Mean Absolute Deviation Examples

Example 1 easy

Calculate the Mean Absolute Deviation (MAD) for [formula] and explain what it measures.

Example 3 easy

Calculate MAD for daily temperatures (ยฐF): [formula].

Example 4 hard

Data set A: [formula] and Data set B: [formula]. Both have mean 5. Calculate MAD for each and explai

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