Introduction to Statistics: Data Classification and Levels of Measurement

Chapter 1: Introduction to Statistics

Chapter Outline

• An Overview of Statistics

• Data Classification

• Data Collection and Experimental Design

Section 1.2: Data Classification

Section Objectives

• Distinguish between qualitative data and quantitative data.

• Classify data according to the four levels of measurement: nominal, ordinal, interval, and ratio.

Types of Data

Qualitative Data

Qualitative data consists of attributes, labels, or non-numerical entries. These data describe qualities or categories and cannot be measured numerically.

• Examples:

  • Major (e.g., Biology, Mathematics)

  • Place of birth (e.g., New York, California)

  • Eye color (e.g., Blue, Brown)

Quantitative Data

Quantitative data consists of numerical measurements or counts. These data can be measured and expressed numerically.

• Examples:

  • Age (e.g., 21 years)

  • Weight of a letter (e.g., 15 grams)

  • Temperature (e.g., 22°C)

Classifying Data by Type: Example

The following table shows sports-related head injuries treated in U.S. emergency rooms during a recent five-year span for several sports. The type of sport is qualitative data, while the number of head injuries treated is quantitative data.

Sport	Head injuries treated
Basketball	131,930
Baseball	83,522
Football	220,258
Gymnastics	33,265
Hockey	41,450
Soccer	98,710
Softball	41,216
Swimming	44,815
Volleyball	13,848

• Qualitative Data: Sport (e.g., Basketball, Soccer)

• Quantitative Data: Head injuries treated (e.g., 131,930)

Levels of Measurement

Nominal Level

The nominal level of measurement consists of qualitative data only. Data are categorized using names, labels, or qualities. No mathematical computations can be made.

• Examples:

  • Movie genres (e.g., Action, Comedy, Drama)

  • Eye color

Ordinal Level

The ordinal level of measurement consists of qualitative or quantitative data. Data can be arranged in order or ranked, but differences between data entries are not meaningful.

• Examples:

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

  • Movie ratings (e.g., 1st, 2nd, 3rd place)

Interval Level

The interval level of measurement consists of quantitative data. Data can be ordered, and differences between data entries are meaningful. However, zero represents a position on a scale, not an inherent zero; zero does not imply "none".

• Examples:

  • Years in which the New York Yankees won the World Series (e.g., 1923, 1927, 1928)

  • Temperature in Celsius or Fahrenheit

Ratio Level

The ratio level of measurement is similar to the interval level, but with an inherent zero (zero implies "none"). Ratios of two data values can be formed, and one data value can be expressed as a multiple of another.

• Examples:

  • Number of World Series victories

  • Weight, height, age

Summary Table: Four Levels of Measurement

Level of Measurement	Put Data in Categories	Arrange Data in Order	Subtract Data Values	Determine if Data Value is a Multiple of Another
Nominal	Yes	No	No	No
Ordinal	Yes	Yes	No	No
Interval	Yes	Yes	Yes	No
Ratio	Yes	Yes	Yes	Yes

Key Formulas and Concepts

• Difference between interval and ratio:

  • Interval: $x - y$ is meaningful, but $x / y$ is not.

  • Ratio: Both $x - y$ and $x / y$ are meaningful, and zero is absolute.

Examples and Applications

• Classifying Data:

  • Eye color: Nominal

  • Ranking of movies: Ordinal

  • Temperature: Interval

  • Weight: Ratio

Additional info: The notes are based on the textbook "Elementary Statistics" and provide foundational concepts for understanding types of data and levels of measurement, which are essential for further study in statistics.