Various answers to this question are possible.
The mean absolute deviation (MAD) is a measure of the dispersion or spread of a sample or a population. So one of its purposes is as a measure.
As such it's an alternative to the standard deviation that is said to be more robust in the sense that the sample MAD can be used to provide more accurate estimates of the population dispersion because it is less sensitive to outliers.
Beyond this, some distributions that have no standard deviations do have MADs; for example, the Cauchy. This means that the dispersions of virtually all distributions can be compared in terms of their MADs.
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An absolute mean is a mean of the absolute magnitude of a function with both positive and negative values.
None.The mean of a single number is itself.Therefore deviation from the mean = 0Therefore absolute deviation = 0Therefore mean absolute deviation = 0None.The mean of a single number is itself.Therefore deviation from the mean = 0Therefore absolute deviation = 0Therefore mean absolute deviation = 0None.The mean of a single number is itself.Therefore deviation from the mean = 0Therefore absolute deviation = 0Therefore mean absolute deviation = 0None.The mean of a single number is itself.Therefore deviation from the mean = 0Therefore absolute deviation = 0Therefore mean absolute deviation = 0
Absolute adjective absolute meaning the one thing you are looking for.
no the standard deviation is not equal to mean of absolute distance from the mean
interquartile range or mean absolute deviation.