One can define dispersion and measure it in different ways. The common dispersion definition is: “way to measure variation of data”. In general, if the dispersion is large then the variation of variable values will be huge. If the dispersion is small, then the variation is close.
Different Measures of Dispersion
The measures of dispersion can be classified into two types namely Absolute measures of dispersion and Relative measures of dispersion. Rest of the article covers these two types in detail.
Absolute Measures of Dispersion
The statistical data observations will generally be specified in some units. If the dispersion values have to be specified in the same units as that of the statistical data, then you have to choose an absolute measure of dispersion. For example, if the statistical data is represented in grams then the measure of dispersion must also be in grams.
There are various absolute measures of dispersion. Commonly used absolute measures are:
• Range
• Mean Deviation
• Variance and Standard Deviation
Here is an overview and example of one absolute measure called Range:
The Range is the simplest measure of dispersion. It is the difference between the top most value and the lowest value in the statistical set of data provided. For example, Jackson took 5 Mathematics tests in one period of time. The test marks are: 70, 60, 50, 80, and 90. What is the range of the marks? The range is calculated by subtracting the lowest value 50 from the highest value 90 and the result will be 40. Thus, the range is 40.
Relative Measures of Dispersion
If you have to compare dispersion of two or more statistical data sets which are of different units, then you have to opt for relative measures of dispersion. These dispersion measures are dimensionless and they are used to establish dispersion relation between any data sets. Common relative measures of dispersion are:
• Coefficient of Range
• Coefficient of Mean Deviation
• Coefficient of Variation
• Coefficient of Standard Deviation
Here is an overview and example of one absolute measure called Coefficient of Variation:
The coefficient of variation is the percentage of variation obtained by dividing standard deviation by mean. For example, a school has two sections for X standard. The average score of students in first section are 85 and the second section average scores are 80. The standard deviations of the two sections are 8 and 7 respectively. Which X standard section has large variation in its scores?
In this problem, the average score denotes the mean and the values of standard deviation are also specified. Now to find the variation of data by calculating coefficient of variation:
Coefficient of variance of section A is 9.4%, which is obtained by dividing standard deviation value 8 by the mean 85 and multiplying the result 0.2 by 100.
Coefficient of variance of section B is 8.75%, which is obtained by dividing 7 by 80 and multiplying the result by 100.
Comparing both the coefficients, section A is consistent when compared to section B. Hence, section B has large variation in its scores.
Different Measures of Dispersion
The measures of dispersion can be classified into two types namely Absolute measures of dispersion and Relative measures of dispersion. Rest of the article covers these two types in detail.
Absolute Measures of Dispersion
The statistical data observations will generally be specified in some units. If the dispersion values have to be specified in the same units as that of the statistical data, then you have to choose an absolute measure of dispersion. For example, if the statistical data is represented in grams then the measure of dispersion must also be in grams.
There are various absolute measures of dispersion. Commonly used absolute measures are:
• Range
• Mean Deviation
• Variance and Standard Deviation
Here is an overview and example of one absolute measure called Range:
The Range is the simplest measure of dispersion. It is the difference between the top most value and the lowest value in the statistical set of data provided. For example, Jackson took 5 Mathematics tests in one period of time. The test marks are: 70, 60, 50, 80, and 90. What is the range of the marks? The range is calculated by subtracting the lowest value 50 from the highest value 90 and the result will be 40. Thus, the range is 40.
Relative Measures of Dispersion
If you have to compare dispersion of two or more statistical data sets which are of different units, then you have to opt for relative measures of dispersion. These dispersion measures are dimensionless and they are used to establish dispersion relation between any data sets. Common relative measures of dispersion are:
• Coefficient of Range
• Coefficient of Mean Deviation
• Coefficient of Variation
• Coefficient of Standard Deviation
Here is an overview and example of one absolute measure called Coefficient of Variation:
The coefficient of variation is the percentage of variation obtained by dividing standard deviation by mean. For example, a school has two sections for X standard. The average score of students in first section are 85 and the second section average scores are 80. The standard deviations of the two sections are 8 and 7 respectively. Which X standard section has large variation in its scores?
In this problem, the average score denotes the mean and the values of standard deviation are also specified. Now to find the variation of data by calculating coefficient of variation:
Coefficient of variance of section A is 9.4%, which is obtained by dividing standard deviation value 8 by the mean 85 and multiplying the result 0.2 by 100.
Coefficient of variance of section B is 8.75%, which is obtained by dividing 7 by 80 and multiplying the result by 100.
Comparing both the coefficients, section A is consistent when compared to section B. Hence, section B has large variation in its scores.
