The Mean Deviation:
          The mean deviation or the average deviation is defined as the mean of the absolute deviations of observations from some suitable average which may be the arithmetic mean, the median or the mode. The difference () is called deviation and when we ignore the negative sign, this deviation is written as  and is read as mod deviations. The mean of these mod or absolute deviations is called the mean deviation or the mean absolute deviation. Thus for sample data in which the suitable average is the, the mean deviation () is given by the relation:
                       
            For frequency distribution, the mean deviation is given by
                       
            When the mean deviation is calculated about the median, the formula becomes
                       
            The mean deviation about the mode is
                       
            For a population data the mean deviation about the population mean  is
                       
            The mean deviation is a better measure of absolute dispersion than the range and the quartile deviation.
            A drawback in the mean deviation is that we use the absolute deviations  which does not seem logical. The reason for this is that  is always equal to zero. Even if we use median or mode in place of , even then the summation  or will be zero or approximately zero with the result that the mean deviation would always be either zero or close to zero. Thus the very definition of the mean deviation is possible only on the absolute deviations.
            The mean deviation is based on all the observations, a property which is not possessed by the range and the quartile deviation. The formula of the mean deviation gives a mathematical impression that is a better way of measuring the variation in the data. Any suitable average among the mean, median or mode can be used in its calculation but the value of the mean deviation is minimum if the deviations are taken from the median. A series drawback of the mean deviation is that it cannot be used in statistical inference.

Coefficient of the Mean Deviation:
          A relative measure of dispersion based on the mean deviation is called the coefficient of the mean deviation or the coefficient of dispersion. It is defined as the ratio of the mean deviation to the average used in the calculation of the mean deviation. Thus
  

Example:
            Calculate the mean deviation form (1) arithmetic mean (2) median (3) mode in respect of the marks obtained by nine students gives below and show that the mean deviation from median is minimum.
            Marks (out of 25): 7, 4, 10, 9, 15, 12, 7, 9, 7
Solution:
            After arranging the observations in ascending order, we get
            Marks: 4, 7, 7, 7, 9, 9, 10, 12, 15
           
           
                             
            (Since  is repeated maximum number of times)

Marks
Total

           
           
           
            From the above calculations, it is clear that the mean deviation from the median hast the least value.

Example:
            Calculate the mean deviation from mean and its coefficients from the following data.

Solution:
            The necessary calculation is given below: