Statistics >> Measures of Dispersion
The other aspects of frequency distribution which we shall consider here are dispersion or variability of the observations. A measure of central tendency does not give the complete information about some distribution and we should use measure of dispersion to supplement the information. Measures of dispersion give an idea about the scattering of values around the central value of the data. The measures of dispersion are called averages of second order. These measures should attain large values if the observations are widely scattered from the centre and should have small values for the data having observation close to the mean.
There are two types of measures of dispersion.
(i) Absolute measure
(ii) Relative measure.
The absolute measures of dispersion are used to measure the variability of a given data expressed in same unit, while the relative measures are used to compare the variability of two or more sets of observations expressed in different units.
There are four absolute measures of dispersion and they are
(i) Range
(ii) Quartile Deviation (Q.D.) or semi-interquartile range
(iii) Mean deviation (MO)
(iv) Standard deviation (SO)
The relative measures are their coefficients.
RANGE
The difference between the largest and smallest values of a set of data is known as Range.
Range = L-S
Co-efficient of Range = L-S/L+S
Merits and Dements of Range
Merits
(i) It is the simplest measure of dispersion.
(ii) It is easy to understand and calculate.
(iii) It is rigidly defined.
Demerits
(i) It is not based on all observations. It is based on two extreme observations only.
(ii) It is affected much by fluctuations of sampling.
(iii) It is not capable of further algebraic treatment.
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