Mean Absolute Deviation (MAD) Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Mean Absolute Deviation (MAD).

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

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.

Find how far each number is from the mean (ignoring +/-), then average those distances. It tells you: on average, how far is a typical value from the center?

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: MAD is the average of the absolute deviations from the mean. Using absolute values prevents positive and negative deviations from canceling each other out.

Common stuck point: Students forget to take absolute values before averaging, which causes deviations to cancel and gives zero — making all data sets look identical.

Sense of Study hint: When calculating MAD, first find the mean \bar{x} of the dataset. Then subtract the mean from each data value and take the absolute value: |x_i - \bar{x}|. Finally, average all the absolute deviations: MAD = \frac{1}{n}\sum |x_i - \bar{x}|.

Worked Examples

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: \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, |6-8|=2, |8-8|=0, |10-8|=2, |12-8|=4.
  3. 3
    Step 3: Find the mean of these absolute deviations: MAD = \frac{4+2+0+2+4}{5} = \frac{12}{5} = 2.4.

Answer

MAD = 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.

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.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

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

Example 2

hard
A teacher claims that adding the same constant to every value in a data set does not change the MAD. Test this claim with the data set {5, 10, 15, 20, 25} by adding 100 to each value and comparing the MADs.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

meanabsolute value