To find the absolute deviation of a value from a data set, you subtract each data point from that value, take the absolute value of each difference, and then compute the average of those absolute differences.
Given the data set \({6, 22, 14, 9, 11, 4}\) and the value \(4\):
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Calculate the absolute deviations:
- |6 - 4| = |2| = 2
- |22 - 4| = |18| = 18
- |14 - 4| = |10| = 10
- |9 - 4| = |5| = 5
- |11 - 4| = |7| = 7
- |4 - 4| = |0| = 0
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List of absolute deviations: {2, 18, 10, 5, 7, 0}
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Average of absolute deviations: \[ \text{Average} = \frac{2 + 18 + 10 + 5 + 7 + 0}{6} = \frac{42}{6} = 7 \]
Therefore, the absolute deviation of \(4\) in this data set is \(7\).