Mean Absolute Deviation (MAD) Statistics Example 1

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

Example 1

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

Solution

  1. 1
    Step 1: Find the mean: 4+6+8+10+125=405=8\frac{4+6+8+10+12}{5} = \frac{40}{5} = 8.
  2. 2
    Step 2: Find the absolute deviations from the mean: ∣4−8∣=4|4-8|=4, ∣6−8∣=2|6-8|=2, ∣8−8∣=0|8-8|=0, ∣10−8∣=2|10-8|=2, ∣12−8∣=4|12-8|=4.
  3. 3
    Step 3: Find the mean of these absolute deviations: MAD=4+2+0+2+45=125=2.4MAD = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4.

Answer

MAD=2.4MAD = 2.4.
The mean absolute deviation measures how far data values are from the mean on average. A smaller MAD indicates data clustered closely around the mean, while a larger MAD indicates more spread. MAD uses absolute values to avoid positive and negative deviations cancelling out.

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 2 medium

Two data sets: A = {10, 10, 10, 10, 10} and B = {2, 6, 10, 14, 18}. Both have a mean of 10. Calculat

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.

← All Mean Absolute Deviation (MAD) Examples Mean Absolute Deviation (MAD) Concept