Mean absolute deviation about the mean and interpretation
The main result is mean absolute deviation about the mean, expressed in the original data unit. The arithmetic mean and observation count identify the center and divisor actually used.
To calculate sample or population standard deviation from raw observations, use the Standard Deviation Calculator and follow its own input conventions.
The formula
Find the arithmetic mean, subtract it from each observation, and average the absolute differences. Centering around the first observation helps retain small spreads near a large common offset.
Verified worked example
For 2, 4, and 6, the arithmetic mean is 4. Absolute distances from that mean are 2, 0, and 2, so their mean absolute deviation is 4/3, approximately 1.333333.
How to use this calculator
- Enter observations separated by commas, spaces, or new lines.
- Keep repeated values as repeated entries and use one common measurement unit.
- Read the arithmetic mean and mean absolute deviation; do not interpret this as median absolute deviation.
Mean Absolute Deviation input conventions
Each observation contributes its distance from the arithmetic mean without a sign. Dividing their total by the number of observations gives the average absolute distance in the original unit. Unlike variance, this operation does not square deviations. It therefore avoids reporting a squared unit and gives a different emphasis to extreme distances.
Interpreting mean absolute deviation about the mean
The abbreviation MAD can refer to either mean or median absolute deviation. This page uses the arithmetic mean as its center and averages the absolute distances. It does not take their median or multiply by a normal-consistency scaling factor. Keep every entry in a common measurement unit and include repeated observations as repeated entries. No value is removed simply because it is unusual; the statistic summarizes the list you actually provide.
Assumptions & limitations
What this calculation assumes
- Each observation receives equal weight and distances are measured from the arithmetic mean.
What to keep in mind
- Unweighted descriptive spread about the mean; no median-based robustness estimate.
Common questions
Is this the median absolute deviation?
No. Median absolute deviation uses the median as the center and then takes the median of absolute distances. This page computes an average around the arithmetic mean.
Can all observations be equal?
Yes. Their mean equals every entry, so all absolute distances and the result are zero. One observation also has zero deviation about its own mean.
Does the method ignore unusual observations?
No. Every supplied observation contributes one absolute distance. If an entry looks wrong, investigate it separately rather than assuming this statistic removed it.
Sources & further reading
Reviewed on