Data Classification and Levels of Measurement in Statistics

Section 1.2: Data Classification

Introduction

Data classification is a foundational concept in statistics, essential for organizing, analyzing, and interpreting data. This section covers the distinction between qualitative and quantitative data, and introduces the four levels of measurement: nominal, ordinal, interval, and ratio.

Types of Data

• Qualitative Data: Consists of attributes, labels, or non-numerical entries. Examples: Colors, place of birth, eye color, movie genres.

• Quantitative Data: Consists of numerical measurements or counts. Examples: Age, weight, height, temperature, number of students.

Classifying Data by Type

To classify data, determine whether each value is a label (qualitative) or a measurable quantity (quantitative).

• Example: The table below shows the number of hospital-treated injuries in U.S. emergency rooms by household product. The product names are qualitative data, while the injury counts are quantitative data.

Household Product	Number of Injuries
Stairs, ramps, landings	266,212
Beds, bedframes, mattresses	62,534
Chairs, sofas, sofa beds	53,353
Tables	41,912
Desks	6,924
Dressers, chests, bureaus	6,584
Bookcases, wall units	3,484

Levels of Measurement

Overview

The level of measurement determines the mathematical operations that can be performed on data and the type of statistical analysis that is appropriate. There are four levels: nominal, ordinal, interval, and ratio.

Nominal Level of Measurement

• Data are categorized using names, labels, or qualities.

• No mathematical computations can be made.

• Example: Movie genres (Action, Adventure, Comedy, Drama, Horror).

Ordinal Level of Measurement

• Data can be arranged in order, or ranked.

• Differences between data entries are not meaningful.

• Can be qualitative or quantitative.

• Example: Top five U.S. occupations with the most job growth (ranked list).

Interval Level of Measurement

• Data can be ordered, and meaningful differences between data entries can be calculated.

• Zero represents a position on a scale, not an inherent zero (does not mean "none").

• Example: Years in which the New York Yankees won the World Series (e.g., 1923, 1927, 1932, etc.).

Ratio Level of Measurement

• Data can be ordered, meaningful differences can be found, and a true zero exists.

• One data value can be expressed as a multiple of another.

• Example: Number of home runs hit by American League baseball teams in a season.

Summary Table: Four Levels of Measurement

Level of Measurement	Qualitative Only	Order Meaningful	Differences Meaningful	Ratio of Values Meaningful
Nominal	Yes	No	No	No
Ordinal	Yes	Yes	No	No
Interval	No	Yes	Yes	No
Ratio	No	Yes	Yes	Yes

Practice Questions

1. Determine whether the data are qualitative or quantitative. Explain your reasoning.

   • Weigh of dogs at an animal rescue facility

   • Carrying capacities of flatbed trucks

   • Hair colors of classmates

   • Student ID numbers

2. Determine the level of measurement of the data set. Explain your reasoning.

   • The years that a television show won the Emmy for best comedy series are listed: 2001, 2003, 2005, 2007, 2011, 2013, 2014, 2016

3. The top ten business schools in the United States for a recent year according to Forbes are listed. (List of schools provided.)

4. The flight numbers of 21 departing flights from Chicago O'Hare International Airport on an afternoon in October of 2016 are listed.

5. The lengths (in seconds) of songs on an album are listed.

Key Formulas and Concepts

• No specific formulas are required for data classification, but understanding the properties of each level is essential for proper statistical analysis.

Additional info:

• When analyzing data, always consider the context and the type of variable to determine the appropriate level of measurement.

• Statistical methods and graphical representations depend on the data type and level of measurement.