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Measures of Dispersion from Average

Recall that dispersion was defined as the extent to which values differ from their average. Range and Quartile Deviation do not attempt to calculate, how far the values are, from their average. Yet, by calculating the spread of values, they do give a good idea about the dispersion. Two measures which are based upon deviation of the values from their average are Mean Deviation and Standard Deviation. Since the average is a central value, some deviations are positive and some are negative. If these are added as they are, the sum will not reveal anything. In fact, the sum of deviations from Arithmetic Mean is always zero. Look at the following two sets of values.
Set A : 5, 9, 16
Set B : 1, 9, 20
You can see that values in Set B are farther from the average and hence more dispersed than values in Set A. Calculate the deviations from Arithmetic Mean and sum them up. What happened? Repeat the same with Median. Is it possible to comment the quantum of variation from the calculated values? Mean Deviation tries to overcome this problem by ignoring the signs of deviations, i.e., it considers all deviations positive. For standard deviation, the deviations are first squared and averaged and then square root of the average is found. In detailed way, We shall discuss them separately.

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