Measure a dataset's typical absolute distance from its arithmetic mean. The result panel keeps mean absolute deviation and its numerical trail together.
For 8, 10, 13, 13, and 16, the mean is 12. Distances from 12 are 4, 2, 1, 1, and 4; their average is 12/5 = 2.4.
MAD provides a compact description of consistency in scores, production measurements, delivery times, or any numerical series. Two groups can share a mean while having very different deviations. A related application of Mean Absolute Deviation is standard-deviation distance.
Mean absolute deviation, or MAD, averages the absolute distances between observations and their mean. Because those distances retain the original unit, MAD is often easier to explain than variance. For a connected concept in Mean Absolute Deviation, see mean and standard deviation.
Reading mean absolute deviation correctly starts with the mathematical structure described here.
Do not let positive and negative deviations cancel. Absolute values are taken before averaging. Also distinguish this quantity from median absolute deviation, a robust statistic centered on the median.
Keep any applicable units beside the source values; the browser cannot detect a silent mismatch during mean absolute deviation.
Find the arithmetic mean, subtract it from each observation, replace each signed difference with its magnitude, add the magnitudes, and divide by the observation count. A hand-worked extension of Mean Absolute Deviation is weighted center.
Before entering data values, identify what each field represents. Its label determines how the mean absolute deviation relationship interprets the entry. The browser cannot supply missing unit context, so preserve that context in your notes.
Adding the same constant to every observation shifts the mean but leaves MAD unchanged. Multiplying all values by a factor multiplies MAD by that factor's absolute value. That behavior gives the mean absolute deviation output a built-in reasonableness test.
A final answer should carry enough context to be reusable: name it mean absolute deviation, attach any applicable unit, and record the rounding point. If another person must reproduce the result, the supplied input in the field and the displayed formula are more informative than the decimal alone.
Mean absolute deviation centers on the arithmetic mean. Median absolute deviation centers on the median and is usually more resistant to a small number of extreme observations. Writing “Mean absolute deviation” beside the output prevents that mix-up.
A useful note for this result contains the supplied inputs (data values), the answer label, and the chosen precision. That record can be checked without recreating the entire page state.
The same units as the original data because distances are not squared.
Yes, exactly when all observations equal their mean.
No. Standard deviation squares deviations before averaging and then takes a square root.
Yes, though its influence grows linearly rather than quadratically as in variance.
They prevent deviations below and above the mean from canceling.