Statistics (Measures of Center & Variability) • Topic 2 of 4

Mean Absolute Deviation (MAD)

Mean Absolute Deviation (MAD) measures how spread out the data is — the average distance each data point is from the mean.

Steps to calculate MAD:

  1. Find the mean of the dataset
  2. Find each data point's absolute distance from the mean: |value - mean|
  3. Find the mean of those distances

A smaller MAD means data is clustered near the mean (consistent). A larger MAD means data is spread out.

CALCULATING MAD:

Data: {2, 4, 4, 6, 9}  Mean=5

  |2-5| = 3
  |4-5| = 1
  |4-5| = 1
  |6-5| = 1
  |9-5| = 4
  --------
  Sum = 10
  MAD = 10/5 = 2

Interpretation: On average, each value is 2 units away from the mean of 5.
Solved Examples
1
Worked Example
Find MAD for {10, 12, 14, 16}.
SolutionMean = 13. Distances: |10-13|=3, |12-13|=1, |14-13|=1, |16-13|=3. Sum=8. MAD=8/4=2.
2
Worked Example
Class A scores (Mean=80, MAD=6) vs Class B (Mean=80, MAD=18). Which is more consistent?
SolutionClass A has smaller MAD, so it is more consistent (scores are closer to the mean).

Key Points

  • MAD = average of all |data point - mean| values
  • Smaller MAD = data is more consistent/clustered
  • Larger MAD = data is more spread out
  • MAD is always non-negative
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The Mean Absolute Deviation (MAD) measures the ___ of data.
Explanation: Spread.
Q2.MAD is the average of the absolute ___ from the mean.
Explanation: Absolute differences.
Q3.A larger MAD means:
Explanation: More spread.
Q4.To find MAD, first find the:
Explanation: The mean.
Practice more MCQs → 📝 Assignment · 35 marks