1.

Give the comparison of alternative measure of dispersion.

Answer»

Comparison of alternative measure of the dispersion has been discussed below.
1. Rigidly defined:
All the four measures the range, quartile deviation, mean deviation & standard deviation are rigidy defined. There is no Vagueness in their definitions.

2. Ease of calculation:
The range is the easiest one to calculate. Quartile deviation requires calculation of the upper & lower quartiles but that is also easy enough. However, the mean deviation & standard deviation require a little more systematic calculation they, too are easy.

3. Simple interpretaion:
All measures of dispersion are easy to interpret. While the range and quartile deviation measure disperrsion in a general way the mean deviation and standard deviation measure dispersion in terms of deviation from a central value. Thus the mean deviation and standard deviation give a better idea about the dispersion of values within the range.

4. Based on all values:
The range and Quantile deviation do not depend on all values where as the mean deviation and standard deviation use all values of the variable the range is affected the most by extreme values.

5. Amendable to algebraic treatment:
The standard deviation is perhaps the earliest for analytical work. Other measure can be also dealt with analytically but derivation are harder.



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