Measures of Dispersion

Dispersion means spread or variability in the values of the items in the given data. usually, the variability measures the degree of sacredness of the observations in a distribution around the central values.

The measure of central tendency indicates the location of the central position of the values in a series and it gives no idea about the variability of data. Let us consider the following distribution:

 

Observations

Mean

Median

Mode

Series: A

6, 8, 9, 11, 11  13, 14, 16

11

11

11

Series: B

1, 5, 10 11, 11, 11, 16, 23

11

11

11

the mean, median and mode of above two series A and B are same. From these central values we cannot determine 11 is the central values of series A or series B. We notice that the variations about the central values are more in the second distribution in comparison to the first. The distributions may have same average but have different variability.

Absolute and Relative Measure of Dispersion

If the units of measures of dispersion are the same as the units of given series, such type of measure of dispersion is known as absolute measure of dispersion. It is use for comparing the variability of series having same units.

The relative measure of dispersion are obtained as the ratio of absolute measure of dispersion to the suitable average and are thus a pure number independent of units.

Characteristics of Good Measure of Dispersion

The following are the characteristics of good measure of dispersion:

-       It should be rigidly defined.

-       It should be easy to understand and simple to calculate.

-       It should be based on all observation.

-       It should be suitable for further mathematical treatment.

-       It should be least affected by fluctuation of sampling.

-       It should be least affected by the extreme values.

Various Types of Measure of Dispersion

The following are the various types of measures dispersion.

            i) Range

            ii) Quartile deviation or semi-inter quartile range

            iii) Mean deviation

            iv) Standard deviation

Range

Range is the simplest method of studying the dispersion. It is the difference between the largest and smallest item.  

range = Largest item – Smallest item

The range is the absolute measure of dispersion. To the variability of two series having different units, the relative measure of range called the coefficient of range is used.