MEASURES OF DISPERSION IN STATISTICS : Dispersion, meaning and definition; Importance; Relative and absolute measures of dispersion.
Dispersion indicates the measure of the extent to which individual items differ. It indicates lack of uniformity in the size of items.
ACCORDING TO BROOK AND DICKS
“Dispersion is the degree of the variation of the variable about a central value.”
ACCORDING TO SIMPSON AND KAFKA
“The measurement of the scatterness of the mass of figures in a series about an average is called a measure of variation or dispersion.”
ACCORDING TO W.I. KING
” The term dispersion is based to indicate the facts that within a given group, the items differ from one another in size or in other words, there is lack of uniformity in their size.”
FEATURES OF DISPERSION
1. It involves different methods through which variations can be measured in quantitative manner.
2. It deals with statistical series.
3. It indicates the degree to which various items of a series deviate from its central value.
4. It supplements the measures of central tendency in revealing the characteristics of a frequency distribution.
5. It speaks of the reliability of the average value of a series.
OBJECTIVES OR IMPORTANCE OR USES OF MEASURES OF DISPERSION
1. To Measure the Reliability of an Average: Dispersion tells us how far an average is representative of the mass of the data. When the dispersion is small, the average is a typical value in the sense that it is a good estimate of the average in the universe from which the data have been taken.
2. To Serve as a Basis for Control of the Variability: In order to control the variation or dispersion of a phenomenon it is necessary to determine the nature and cause of variation. The measurement of inequality in the distribution of income and wealth requires the measures of variation Similarly variations in body temperature, blood pressure etc., are noted for proper diagnosis.
3. To Compare two or more Series with Regard to their Variability: The study of dispersion is essential for determining the degree of consistency, uniformity, reliability etc.. A low degree of variation means more uniformity, consistency, reliability of data, whereas a high degree of variation lacks uniformity, consistency, reliability etc.
4. To Facilitate the use of Other Statistical Techniques: The study of dispersion helps in the application of various statistical tools like correlation, regression, statistical quality control etc.
5. To establish trend in time series: Dispersion helps to find out the trend and remove seasonal, cyclical and random fluctuations.
CHARACTERISTICS OF A GOOD MEASURE OF DISPERSION
A good measure of dispersion should possess the following characteristics:
- It should be simple to understand.
- It should be easy to calculate.
- It should be rigidly defined.
- It should be based on each and every item of the distribution.
- It should be suitable for algebraic and arithmetical manipulation.
- It should have sampling stability.
- It should not be unduly affected by extreme items.