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Measures Of Dispersion

Question
CBSEENST11024827

Comparison of alternative measures of the dispersion has been discussed below:

Solution

1. Rigidly defined : All the four measures-the range, quartile deviation, mean deviation and standard deviation are rigidly defined. There is no vagueness in their definition.

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

3. Simple interpretation : All measures of dispersion are easy to interpret. While the range and quartile deviation measure dispersion in a general way the mean deviation and standard deviation measure dispersion in terms of deviations 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 quartile deviation do not depend on all values, whereas, 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 easiest for analytical work. Other measures can be also dealt with analytically but derivation are harder.