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Quartile Deviation

Quartile Deviation (Q. D.) is half of the difference between the first and third quartiles. Hence, it is called Semi Inter Quartile Range. 

In Symbols,   Q. D = Q3 – Q1 

Among the quartiles Q1, Q2 and Q3, the range Q3 Q1 is called inter quartile range and (Q3-Q1)/2 , Semi inter-quartile range.

Co-efficient of Quartile Deviation:

               Co-efficient of Q. D = (Q3-Q1)/(Q3+Q1)

Mean Deviation:

The range and quartile deviation are not based on all observations. They are positional measures of dispersion. They do not show any scatter of the observations from an average. 

The mean deviation is measure of dispersion based on all items in a distribution. 

Definition: Mean deviation is the arithmetic mean of the deviations of a series computed from any measure of central tendency; i.e., the mean, median or mode, all the deviations are taken as positive i.e., signs are ignored. 

“Mean deviation is the average amount of deviation of the items in a distribution from either the median or the mean, ignoring the signs of the deviations”. We usually compute mean deviation about any one of the three averages mean, median or mode. Some times mode may be ill defined and as such mean deviation is computed from mean and median. Median is preferred as a choice between mean and median. But in general practice and due to wide applications of mean, the mean deviation is generally computed from mean. Mean deviation is denoted by M.D. 

Coefficient of mean deviation: Mean deviation calculated by any measure of central tendency is an absolute measure. For the purpose of comparing variation among different series, a relative mean deviation is required. The relative mean deviation is obtained by dividing the mean deviation by the average used for calculating mean deviation.

Coefficient of mean deviation: 

                                

If the result is desired in percentage, the coefficient of mean deviation