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Absolute and Relative Measures of Dispersion

All the measures, described so far, are absolute measures of dispersion. They calculate a value which, at times, is difficult to interpret.

For example, consider the following two data sets:
Set A       500      700       1000
Set B     100000   120000 130000

Suppose the values in Set A are the daily sales recorded by an ice cream vendor, while Set B has the daily sales of a big departmental store. Range for Set A is 500 whereas for Set B, it is 30,000. The value of Range is much higher in Set B. Can you say that the variation in sales is higher for the departmental store? It can be easily observed that the highest value in Set A is double the smallest value, whereas for the Set B, it is only 30% higher. Thus absolute measures may give misleading ideas about the extent of variation especially when the averages differ significantly.

Another weakness of absolute measures is that they give the answer in the units in which original values are expressed. Consequently, if the values are expressed in kilometres, the dispersion will also be in kilometres. However, if the same values are expressed in meters, an absolute measure will give the answer in meters and the value of dispersion will appear to be 1000 times.

To overcome these problems, relative measures of dispersion can be used. Each absolute measure has a relative counterpart. Thus, for Range, there is Coefficient of Range which is calculated as follows:
Coefficient of Range = where L = Largest value
S = Smallest value

Similarly, for Quartile Deviation, it is Coefficient of Quartile Deviation which can be calculated as follows:
Coefficient of Quartile Deviation = where Q3=3rd Quartile Q1 = 1st Quartile
For Mean Deviation, it is Coefficient of Mean Deviation.
Coefficient of Mean Deviation =

Thus if Mean Deviation is calculated on the basis of the Mean, it is divided by the Mean. If Median is used to calculate Mean Deviation, it is divided by the Median. For Standard Deviation, the relative measure is called Coefficient of Variation, calculated as below:
Coefficient of Variation =

It is usually expressed in percentage terms and is the most commonly used relative measure of dispersion. Since relative measures are free from the units in which the values have been expressed, they can be compared even across different groups having different units of measurement.

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