Mean Absolute Deviation (MAD) Statistics Example 2

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

Example 2

medium
Two data sets: A = {10, 10, 10, 10, 10} and B = {2, 6, 10, 14, 18}. Both have a mean of 10. Calculate the MAD for each and explain what it tells you.

Solution

  1. 1
    Step 1: Data set A: All values equal the mean (10), so all absolute deviations are 0. MADA=0+0+0+0+05=0MAD_A = \frac{0+0+0+0+0}{5} = 0.
  2. 2
    Step 2: Data set B: Deviations: ∣2−10∣=8|2-10|=8, ∣6−10∣=4|6-10|=4, ∣10−10∣=0|10-10|=0, ∣14−10∣=4|14-10|=4, ∣18−10∣=8|18-10|=8. MADB=8+4+0+4+85=245=4.8MAD_B = \frac{8+4+0+4+8}{5} = \frac{24}{5} = 4.8.
  3. 3
    Step 3: MADA=0MAD_A = 0 means no variability — all values are identical. MADB=4.8MAD_B = 4.8 means values are, on average, 4.8 units from the mean.

Answer

MADA=0MAD_A = 0 (no spread), MADB=4.8MAD_B = 4.8 (considerable spread). Both have the same mean but very different variability.
MAD quantifies variability in intuitive units — it tells you the average distance from the mean. A MAD of 0 means perfect uniformity, while larger values indicate greater dispersion. This makes MAD easier to interpret than variance, which uses squared units.

About Mean Absolute Deviation (MAD)

The Mean Absolute Deviation (MAD) is the average of the absolute distances between each data point and the mean of the dataset. It measures how spread out data values are from the center, with larger MAD values indicating more variability.

Learn more about Mean Absolute Deviation (MAD) →

More Mean Absolute Deviation (MAD) Examples

Example 1 easy

Find the mean absolute deviation (MAD) of the data set: 4, 6, 8, 10, 12.

Example 3 medium

The heights (in cm) of 6 plants are: 12, 15, 14, 18, 13, 16. Calculate the MAD and interpret the res

Example 4 hard

A teacher claims that adding the same constant to every value in a data set does not change the MAD.

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