10 CHAPTER 1 Introduction to Statistics Levels of Measurement Another characteristic of data is their level of measurement. The level of measurement determines which statistical calculations are meaningful. The four levels of measurement, in order from lowest to highest, are nominal, ordinal, interval, and ratio. Data at the nominal level of measurement are qualitative only. Data at this level are categorized using names, labels, or qualities. No mathematical computations can be made at this level. Data at the ordinal level of measurement are qualitative or quantitative. Data at this level can be arranged in order, or ranked, but differences between data entries are not meaningful. DEFINITION When numbers are at the nominal level of measurement, they simply represent a label. Examples of numbers used as labels include Social Security numbers and numbers on sports jerseys. For instance, it would not make sense to add the numbers on the players’ jerseys for the Chicago Bears. Classifying Data by Level For each data set, determine whether the data are at the nominal level or at the ordinal level. Explain your reasoning. (Source: U.S. Bureau of Labor Statistics) 1. Top five U.S. occupations with the most job growth (projected 2029) 1. Home health and personal care aides 2. Fast food and counter workers 3. Restaurant cooks 4. Software developers and software quality assurance analysts and testers 5. Registered nurses 2. Movie genres Action Adventure Comedy Drama Horror SOLUTION 1. This data set lists the ranks of the five fastest-growing occupations in the U.S. over the next few years. The data set consists of the ranks 1, 2, 3, 4, and 5. Because the ranks can be listed in order, these data are at the ordinal level. Note that the difference between a rank of 1 and 5 has no mathematical meaning. 2. This data set consists of the names of movie genres. No mathematical computations can be made with the names, and the names cannot be ranked, so these data are at the nominal level. TRY IT YOURSELF 2 For each data set, determine whether the data are at the nominal level or at the ordinal level. Explain your reasoning. 1. The final standings for the Pacific Division of the National Basketball Association 2. A collection of phone numbers Answer: Page A35 EXAMPLE 2 Picturing the World For more than 30 years, The Harris Poll has conducted an annual study to determine the strongest brands, based on consumer response, in several industries. A recent study determined the top five health nonprofit brands, as shown in the table. (Source: The Harris Poll) Top five health nonprofit brands 1. St. Jude Children’s Research Hospital 2. Make-A-Wish 3. American Cancer Society 4. Shriners Hospital for Children 5. The Breast Cancer Research Foundation In this list, what is the level of measurement?
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