In case of mean absolute deviation every observation is taken into consideration. Mean absolute deviation is the arithmetic mean of all deviations from mean (or alternately from median). If deviations of the values are taken from mean, the mean of these deviations disappears because the sum of deviations from mean is always zero. Therefore in order to keep all the values positive, absolute deviations are used to find the mean of deviations called mean absolute deviation.
Mean absolute deviation from mean for grouped and ungrouped data can be calculated by using the formulas:
Similarly mean absolute deviation from median can be calculated by using the formulas:
Here,   is called modulus
Modulus is used for the purpose of ignoring the signs associated with the values.
For example:
85=3 and also 58=3
Coefficient of Mean Absolute Deviation
Mean absolute deviation is an absolute measure of dispersion whereas coefficient of mean absolute deviation is the relative measure of dispersion. The coefficient of mean absolute deviation is obtained by dividing the mean absolute deviation by the average used in the calculation of deviation.
The concept of Mean absolute deviation from mean, Coefficient of mean absolute deviation from mean, Mean absolute deviation from median, Coefficient of mean absolute deviation from median can be elaborated with the help of following problem.
For Ungrouped Data
Problem: Following are the number of hours a machine worked for the last 9 weeks 47, 63, 75, 39, 10, 60, 96, 32, and 28.

Find mean absolute deviation from mean.

Find coefficient of mean deviation from mean.

Calculate mean absolute deviation from median.

Calculate coefficient of mean deviation from median.
For Grouped Data
Problem: Following are the observations showing the age of 50 employees working in a whole sale center.

Find mean absolute deviation from mean.

Find coefficient of mean deviation from mean.

Calculate mean absolute deviation from median.

Calculate coefficient of mean deviation from median.
Mean Deviation from Mean
Mean Deviation from Median
Thank you for this excellent presentation. I just miss a discussion of its practical use in relation to the standard deviation. Who uses M.D. MAD as it is also recognized and why?
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