Mean Absolute Deviation

Mean Absolute Deviation: How to Solve

Mean absolute deviation (MAD) measures how far a set of values typically is from its mean. The key idea is to find the average of the absolute distances from the mean, so all differences are treated as nonnegative.

Step-by-step method

1. Find the mean of the data set.
2. Subtract the mean from each value.
3. Take the absolute value of each difference.
4. Add the absolute values.
5. Divide by the number of data values.

What to watch for

• Use absolute values so no distance is negative.
• Keep the same order of operations: mean first, then deviations, then average those deviations.
• If the data include repeated values, treat each one separately.

Quick check

Your MAD should be a nonnegative number. If all data values are the same, every deviation is 0, so the MAD is 0. Also, the result should make sense as a typical distance from the mean: larger spread means a larger MAD.

Final simplification

Carry out arithmetic carefully and reduce the final answer if it is a fraction or decimal that can be simplified.