Dispersion
The dispersion is the tendency of data to be scattered over a range. Dispersion is the important feature of a frequency distribution. It is also called spread or variation. Range, variance and standard deviation are all measures of dispersion. Common measure of dispersion are, range, inter quartile range and quartile deviation, average deviation or mean deviation and standard deviation.

Data Dispersion
Measures of dispersion measure how spread out a set of data. It is important to know the amount of dispersion, variation or spread, as data that is more dispersed or separated is less reliable for analytical purposes. Dispersion is depend upon the type of scale used to measure data characteristics that is quantitative or categorical.

Degree of Dispersion
Dispersion may enable to get additional information about the composition of data. A point is that a high degree of uniformity is a desirable quality. Measure of dispersion are useful in comparing two or more distributions in respect to disparities. A greater degree of dispersion mean lack of uniformity or homogeneity in the data while a low degree of dispersion stands for uniformity or homogeneity.


Measures of Dispersion

For the study of dispersion, we need some measures which show whether the dispersion is small or large. There are two types of measure of dispersion which are:

(a) Absolute Measure of Dispersion
(b) Relative Measure of Dispersion

Absolute Measures of Dispersion:

These measures give us an idea about the amount of dispersion in a set of observations. They give the answers in the same units as the units of the original observations. When the observations are in kilograms, the absolute measure is also in kilograms. If we have two sets of observations, we cannot always use the absolute measures to compare their dispersion. We shall explain later as to when the absolute measures can be used for comparison of dispersion in two or more than two sets of data. The absolute measures which are commonly used are:

- The Range
- The Quartile Deviation
- The Mean Deviation
- The Standard deviation and Variance
- Relative Measure of Dispersion:

These measures are calculated for the comparison of dispersion in two or more than two sets of observations. These measures are free of the units in which the original data is measured. If the original data is in dollar or kilometers, we do not use these units with relative measure of dispersion. These measures are a sort of ratio and are called coefficients. Each absolute measure of dispersion can be converted into its relative measure. Thus the relative measures of dispersion are:

1.	Coefficient of Range or Coefficient of Dispersion.
2.	Coefficient of Quartile Deviation or Quartile Coefficient of Dispersion.
3.	Coefficient of Mean Deviation or Mean Deviation of Dispersion.
4.	Coefficient of Standard Deviation or Standard Coefficient of Dispersion.
5.	Coefficient of Variation (a special case of Standard Coefficient of Dispersion)


Solved Example:
The Math test marks of a class are as follows:
52, 45, 25, 75, 63, 86, 72, 85, 55, 65, 70, 82, 90, 48, 68, 86, 65, 64, 78, 75, 32, 42. Find the inter quartile range.

Solution:
Given data:
52, 45, 25, 75, 63, 86, 72, 85, 55, 65, 70, 82, 90, 48, 68, 86, 65, 64, 78, 75, 32, 42

Step 1:
If the marks are arranged in an order:
25	32	42	45	48	52	55	63	64	65	65	68	70	72	75	75	78	82	85	86	86	90
                    a				65                          a
                    Q1				Q2						    Q3

Step 2:
Inter Quartile range = Q3 - Q1 = 78 - 52 = 26
This tells that the middle 50% of the test score are dispersed over a range of 26 marks.