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The answer depends on absolute deviation from what: the mean, median or some other measure.

Suppose you have n observations, x1, x2, ... xn and you wish to calculate the sum of the absolute deviation of these observations from some fixed number c.

The deviation of x1 from c is (x1 - c).

The absolute deviation of x1 from c is |x1 - c|. This is the non-negative value of (x1 - c). That is,

if (x1 - c) ≤ 0 then |x1 - c| = (x1 - c)

while

if (x1 - c) < 0 then |(x1 - c)| = - (x1 - c).

Then the sum of absolute deviations is the above values, summed over x1, x2, ... xn.

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Q: Definition for Sum of Absolute Deviations?
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