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Measures of Dispersion

Dispersion may be defined as the extent of the scatteredness of item around a measure of central tendency.

Methods of measuring dispersion

The following are the methods of measuring dispersion: (i) the range; (ii) the semi-interquartile range or quartile deviation; (iii) the mean deviation; and (iv) the standard deviation.
 
Range
 
It is the difference between the highest and the lowest value in the series, i.e., Range = xh - xl, where xh is highest value and xl is the lowest value. The coefficient of range = (xh - xl)/(xh + xl).

Mean deviation

Individual series
MD = 94992.png
 
where M = median/mean/mode, n = number of observations.
 
Discrete series
MD = 94998.png

 

Note: In general, mean deviation (MD) always stands for mean deviation about the median.

Standard deviation

The arithmetic mean of the square of deviations of the variable values from its actual arithmetic mean is known as variance and its square root is known as standard deviation (σ).
 
Individual series
σ2 = variance = 95006.png
95014.png
 
Discrete series
σ2 = variance = 95020.png
95026.png 
 
Standard deviation
(σ) = 95032.png

 

Note: If di = 95078.png then
σ2 = h2 95084.png




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