Quartile Deviation
The range as a measure of dispersion discussed above has certain limitations. It is based on two extreme items and it fails to take account of the scatter within the range. From this there is reason to believe that if the dispersion of the extreme items is discarded, the limited range thus established might be more instructive for this purpose there has been developed a measure called the interquartile range the range which includes the middle 50 per cent of the distribution that is one quarter of the observations at the lower end another quarter of the observations at the upper end of the distribution are excluded in computing the interquartile range. In other works, interquartile range represents the difference between the third quartile and the first quartile.
Symbolically,
Interquartile range = Q3 – Q1
Very often the interquartile range is reduced to the form of the semi-tier quartile range or quartile deviation by dividing it by 2
Symbolically
Quartile deviation or Q. D = (Q3 – Q1) / 2
Quartile deviation given the average amount by which the two quartiles differ from the median. In asymmetrical distribution the two quartiles Q1 and Q3) are equidistant from the median med - 1 = Q3 – med. And as such the difference can be taken as a measure of dispersion. The median ± covers exactly 50 per cent of the observations.
In reality however one seldom finds a series in business and economic data that is perfectly symmetrical. Nearly all distributions of social series are asymmetrical. In an say metrical distribution Q1and Q3 are not equidistant from the median. As a result an asymmetrical distribution includes only approximately 50 per cent of observations.
When quartile deviation is very small it describes high uniformity or small variation of the central 50% items and a high quartile deviation means that the variation among the central items is large.
Quartile deviation is an absolute measure of dispersion. The relative measure corresponding to this measure, called the coefficient of quartile deviator is calculated as follows.
Coefficient of Q.D = (Q3 – Q1) / 2 / (Q3 + Q1)/2 = Q3 – Q1 / Q3 + Q1
Coefficient of quartile deviation can be used to compare the degree of variation in different distributions.
Computation of quartile deviation the process of computing quartile deviation is very simple we have just to compute the values of the upper and lower quartiles the following illustrations would clarify calculations.