1.2 Data Classification

1. 1.2 Data Classification How to distinguish between qualitative and quantitative data How to classify data with respect to the four levels of measurement: nominal, ordinal, interval, and ratio

2. Qualitative data Qualitative dataconsist of attributes, labels, or nonnumerical entries.

3. Quantitative data Quantitative data consist of numerical measurements or counts.

4. Try it yourself 1 Classifying Data by Type The population of several U.S. cities are shown in the table. Which data are qualitative data and which are quantitative data? (Source: U.S. Census Bureau) The two different data sets consist of the names of the cities and the populations of the cities. The cities consist of nonnumerical data and are therefore qualitative data. The populations are numerical data and are therefore quantitative data.

5. Nominal level of measurement 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.

6. Ordinal level of measurement 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.

7. Try it Yourself 2 Classifying Data by Level Consider the following data sets. For each data set, decide whether the data are at the nominal level or at the ordinal level. • The final standings for the Pacific Division of the National Basketball Association The final standings represent a ranking of basketball teams. Ordinal, because the data can be put in order. • A collection of phone numbers The collection of phone numbers represents labels. Nominal, because no mathematical computations can be made.

8. Interval level of measurement Data at the interval level of measurement can be ordered, and meaningful differences between data entries can be calculated. At the interval level, a zero entry simply represents a position on a scale; the entry is not an inherent zero.

9. Ratio level of measurement Data at the ratio level of measurement are similar to data at the interval level, with the added property that a zero entry is an inherent zero. A ratio of two data values can be formed so that one data value can be meaningfully expressed as a multiple of another.

10. Try it yourself 3 Classifying Data by Level Decide whether the data are at the interval level or at the ratio level. • The body temperatures (in degrees Fahrenheit) of an athlete during an exercise session Interval, because the data can be ordered and meaningful differences can be calculated, but it does not make sense to write a ratio using the temperatures. • The heart rates (in beats per minute) of an athlete during an exercise session Ratio, because the data can be ordered, meaningful differences can be calculated, the data can be written as a ratio, and the data set contains an inherent zero.

11. Levels of measurement The following tables summarize which operations are meaningful at each of the four levels of measurement. When identifying a data set’s level of measurement, use the highest level that applies.