As you know, a measure of dispersion is the average of the deviations of items from its mean i.e., it is an average of second order. Hence, it should also possess all the qualities of a good measure of an average. According to Dispersion Yule and Kendall the qualities of a good measure of dispersion are as follows:

1) Statistical measures are used even by layman. So complicated definitions and calculations are not desirable. It should be simple to understand and easy to calculate.

2) It should be rigidly defined. For the same data, all the methods should produce the same answer. Different methods of computation leading to different answers are not proper.

3) It should be based on all items. Where it is based on all items, it will produce a more representative value. Thus, good measure of dispersion should be based on the entire data.

4) It should be amenable to further algebric treatment. This means combining groups, calculations of missing values, adjustment for wrong entries, etc., which are possible without the knowledge of actual values of all items. Such treatment should be possible with a good measure of dispersion also. 

5) It should have sampling stability. It means that the average difference between the values obtained from the sample and the corresponding values from the population should be the least. If it is so far a measure of dispersion, it is the best Measure.

6) It should not be unduly affected by the extreme items. Extreme items, many times, are not true representatives of the data. So their presence should not affect the calculation to a large extent. This list is not a complete-list of the properties of a good measure of dispersion. But these are the most important characteristics which a good measure of dispersion should possess.

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