Measures of dispersion is statistical measure by which we determine how the observations spread out or scattered on each side of center. Variance and standard deviation is the most popular measures of dispersion.
Definition of Dispersion
Dispersion is a statistical measure that indicates how the observations are spread out or scattered on each side of the center. If the value of the dispersion is small, it indicates the high uniformity of the observations. The absence of dispersion in the data indicates the perfect uniformity. So, this situation arises when all the observations are identical.
According to some scholars, the measure of dispersion is defined as,
Riegelman: Dispersion is the extent to which the magnitude or qualities of the items differ; that is, the degree of diversity.
W.I. King.: The term dispersion is used to indicate the facts that within a given group, the items differ from another in size or other words, there is a lack of uniformity in their size.
Spiegel: The degree to which numerical data tend to spread about an average value is called the variation or dispersion of data.
B.C. Brookes and W.F.L. Dick: Dispersion or spread is the degree of the scatter or variation of the variable about a central value.
Ai- Bewley: Dispersion is the measure of the variation of the items.
A measure of dispersion appears to serve two purposes,
- It is one of the most important quantities used to characterize a frequency distribution.
- It affords a basis of comparision between two or more frequency distribution.
Different types of measures of dispersion
- Interquartile range and quartile deviation
- Mean deviation
- Median absolute deviation
- Standard deviation, and
- Coefficient of variation.
Characteristics of a good measures of dispersion
- It should be based on all the observations.
- It’s unit should the same as the unit of measurement of items.
- It should be rigidly defined.
- It should follow the general rules of mathematics.
- It should not be subjected to complicated and tedious calculations.
Uses of measures of dispersion
- It tells the reliability of a measure of central value.
- It makes it possible to compare two series of data in respect of their variability.
- A measure of dispersion provides the basis for the control of variability.
- It has a wide application in almost all fields of statistics.