Mean Absolute Deviation Math Example 4

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

Example 4

hard
Data set A: {4,5,5,6}\{4, 5, 5, 6\} and Data set B: {1,5,5,9}\{1, 5, 5, 9\}. Both have mean 5. Calculate MAD for each and explain which has greater variability and why.

Solution

  1. 1
    Set A deviations: ∣4−5∣=1,∣5−5∣=0,∣5−5∣=0,∣6−5∣=1|4-5|=1, |5-5|=0, |5-5|=0, |6-5|=1; MADA=2/4=0.5MAD_A = 2/4 = 0.5
  2. 2
    Set B deviations: ∣1−5∣=4,∣5−5∣=0,∣5−5∣=0,∣9−5∣=4|1-5|=4, |5-5|=0, |5-5|=0, |9-5|=4; MADB=8/4=2MAD_B = 8/4 = 2
  3. 3
    Set B has 4× greater MAD (2 vs 0.5) despite same mean
  4. 4
    Interpretation: Set B has much greater spread — values deviate further from the mean on average

Answer

MADA=0.5MAD_A = 0.5, MADB=2.0MAD_B = 2.0. Set B has 4× more variability despite the same mean.
Same mean but different MAD demonstrates that center and spread are independent properties. Set B's extreme values (1 and 9) create large absolute deviations. MAD clearly quantifies this difference while the identical means hide it.

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 →

More Mean Absolute Deviation Examples

Example 1 easy

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

Example 2 medium

Compare MAD and standard deviation for the data [formula]. Calculate both and explain when MAD is pr

Example 3 easy

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

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