Describe spread with mean absolute deviation
The idea
Find the mean by dividing the total of the data values by their count.
Step by step
- Find the mean by dividing the total of the data values by their count.
- Subtract the mean from each value and take the absolute value of each difference.
- Average those distances. A larger mean absolute deviation indicates more spread around the mean.
Example
The data are 2, 4, 4, 8, 12, 12. Their mean is 7. What is the mean absolute deviation? Give an exact simplified value.
Answer
The distances from the mean are 5, 3, 3, 1, 5, 5. Their sum is 22; divide by 6 to get 11/3.
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Compare the sets 4, 5, 6 and 0, 5, 10. Show that they share a mean but have different mean absolute deviations.
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