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Displaying Qualitative Data Sets

Previous Definitions

4. A population is a set of objects or events being studied.

10. Qualitative data are data expressed in categories.

More Definitions

16. A class is one of the categories into which a data set (population) can be put.

17. Class frequency is the data-set (population) count falling within the particular class.

18. Class relative frequency is the data-set (population) count falling within the particular class divided by the data-set total.

An Example of a Qualitative Data Set and Its Display

Motor vehicle models by specific model year (e.g., 2005 Chevrolet Equinox sport-utility vehicle) that made Consumer Reports' Used-Cars-to-Avoid list by reason of high repair frequency may be found on page 26 of Consumer Reports Cars: Used Car Buying Guide 2006. To exhibit this data set of motor vehicle models, we group them by auto manufacturer, making each auto manufacturer a class. Data sets are often exhibited using a table or chart (or both) similar to what follows.

 

Summary Table for CR's Used Cars to Avoid for Model Years 1998 Through 2005
Class Class Frequency Class Relative Frequency
Auto Manufacturer Number of Models on List Fractional Share
General Motors Corporation 192 .36
DaimlerChrysler AG 120 .23
Ford Motor Company 86 .16
Volkswagen AG 74 .14
BMW AG 21 .04
Hyundai Motor Company 11 .02
Nissan Motor Company 9 .02
Mazda Motor Corporation 7 .01
Isuzu Motors Ltd. 4 .01
Porsche AG 4 .01
Honda Motor Company 4 .01
Suzuki Motor Corporation 0 .00
Mitsubishi Motors Corporation 0 .00
Subaru Division of Fuji Heavy Industries Ltd. 0 .00
Toyota Motor Corporation 0 .00

 

 

 

For additional information on the Used Cars to Avoid (for example, what brands contributed most to a manufacturer's total), see "Chevrolet Reliability Worst of Big Three Brands, by CR Measures," Auto on Info, February 2006, and "General Motors and DaimlerChrysler Again Dominate CR's Used-Cars-to-Avoid List," Auto on Info, February 2006.

Pareto's Principle

Note that in the above example 20% of the classes (the automobile manufacturers General Motors, DaimlerChrysler, and Ford) account for about 80% (more precisely, 75%) of the population of Used Cars to Avoid. This lopsidedness occurs frequently enough to have been given several names - Pareto's Principle, Pareto's Law, and the 80-20 Rule. A table exhibiting the 80-20 Rule, or an approximation thereof (such as that above), is referred to as a Pareto table and a bar chart exhibiting the 80-20 Rule, or an approximation thereof (such as that above), is called a Pareto chart, in honor of the late-19th- and early-20th-century Italian economist Vilfredo Pareto, who found that 80% of the wealth of a nation is owned by 20% of its people. Businessmen, economists, sociologists, and academics refer to Pareto's Principle often.

 

 

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