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.
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.
Rework Mean Absolute Deviation without copying Mean absolute deviation. Begin with Data values and preserve the fixed condition. Predict the scale of the Mean Absolute Deviation answer, then compare it with Mean absolute deviation. Store a changed the fixed condition as another Mean Absolute Deviation case.
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.
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.
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.
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.
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.
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.