Average Deviation
Absolute Deviation
The absolute deviation is the absolute difference between each value of the statistical variable and the arithmetic mean.
D_{i} = |x - x|
Average Deviation
The average deviation is the arithmetic mean of the absolute deviations.
The average deviation is represented by
Example
Calculate the average deviation of the following distribution:
9, 3, 8, 8, 9, 8, 9, 18
Average Deviation for Grouped Data
If the data is grouped in a frequency table, the expression of the average deviation is:
Example
Calculate the average deviation of the following distribution:
x_{i} | f_{i} | x_{i }· f_{i} | |x - x| | |x - x| · f_{i} | |
[10, 15) | 12.5 | 3 | 37.5 | 9.286 | 27.858 |
---|---|---|---|---|---|
[15, 20) | 17.5 | 5 | 87.5 | 4.286 | 21.43 |
[20, 25) | 22.5 | 7 | 157.5 | 0.714 | 4.998 |
[25, 30) | 27.5 | 4 | 110 | 5.714 | 22.856 |
[30, 35) | 32.5 | 2 | 65 | 10.714 | 21.428 |
21 | 457.5 | 98.57 |
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