Mean Absolute Deviation Examples in Math

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

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

Concept Recap

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.

Standard deviation can feel abstract with its squaring and square roots. MAD is simpler: just ask 'on average, how far is each data point from the center?' If the mean test score is 80 and the MAD is 5, a typical student scored about 5 points away from 80—some above, some below.

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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 measures spread by averaging absolute deviations. Unlike range (which uses only two values), MAD uses every data point. Unlike standard deviation, MAD doesn't square the deviations—it's more intuitive but less common in advanced statistics.

Common stuck point: Don't forget the absolute value! Without it, positive and negative deviations cancel out, and you always get zero.

Worked Examples

Example 1

easy
Calculate the Mean Absolute Deviation (MAD) for \{2, 5, 7, 10, 6\} and explain what it measures.

Solution

  1. 1
    Mean: \bar{x} = (2+5+7+10+6)/5 = 30/5 = 6
  2. 2
    Absolute deviations: |2-6|=4, |5-6|=1, |7-6|=1, |10-6|=4, |6-6|=0
  3. 3
    MAD = \frac{4+1+1+4+0}{5} = \frac{10}{5} = 2
  4. 4
    Interpretation: on average, each value is 2 units away from the mean

Answer

MAD = 2. On average, each data point deviates from the mean by 2 units.
MAD measures the average absolute distance of data points from the mean. Unlike variance (which squares deviations), MAD keeps deviations in the original units. It is more interpretable than variance and more resistant to extreme values than variance.

Example 2

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

Practice Problems

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

Example 1

easy
Calculate MAD for daily temperatures (°F): \{68, 72, 65, 75, 70\}.

Example 2

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

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

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