First Moment of Dispersion or Mean Deviation

Mean deviation or the average deviation is the measure if dispersion which   is based upon all the items in a variable .It is the arithmetic mean of the deviations of the values from a measure of central tendency   In the words of Clark and schkade average deviation is the average amount of scatter of items distribution from either mean or the median ignoring sings of the deviations.

Thus it is a measure obtained by calculating the absolute deviations of each observation from the media or the mean, taking all deviations as positive, and then averaging these decimations by taking their arithmetic mean. Mean deviation from arithmetic mean is also called first moment of dispersion.

The following process is adopted for its calculation:

(1)   Choice of Average : Theoretically mean deviation may be computed from any average mean or median or mode but in practice median and mean   are popular, of the two the use of median is better since sum of the deviations of observations is the least from median, as such unless specifically    nothing is given in the question median should be used.

(2)   Ignoring sings:  In its computation the algebraic sings of the deviations are ignored i.e. all the deviations are taken as positive. To indicate deviations are absolute and sings are ignored.

(3)   Mean of the Deviations:  The total of sum of the deviations is divided by the number of items, the quotient or the result is the mean deviation.

(4)   Formula: Mean deviation is expressed by the greek letter small delta as such.

(5)   Mean deviation from Mean

(6)   Mean deviation from Median

(7)   Mean deviation from Mode

Coefficient of Mean Deviation: The purpose of comparing variations or dispersal between two or more different sets of data a relative measure is computed using the following formula .

Coefficient of mean deviation from mean =x/x

Coefficient of mean deviation from median=m/m

Coefficient of mean deviation from mode= z/z