3.1 Categorical, Ordinal, and Quantitative Data

Data types are crucial in understanding and analyzing information effectively. Categorical, ordinal, and quantitative data each have unique characteristics that shape how we interpret and visualize them. Knowing these differences is key to choosing the right analysis methods.

This topic builds on the foundation of data structures, diving into specific data types. It explains how to classify data based on its properties and scale of measurement, which is essential for accurate data representation and meaningful insights.

Types of Data

Categorical and Nominal Data

Top images from around the web for Categorical and Nominal Data

• 

  graphics - Good Ways to Visualize Longitudinal Categorical Data in R - Stack Overflow View original

  Is this image relevant?

• 

  Documentation/4.1/Developers/Charts - Slicer Wiki View original

  Is this image relevant?

• 

  graphics - Good Ways to Visualize Longitudinal Categorical Data in R - Stack Overflow View original

  Is this image relevant?

• 

  Documentation/4.1/Developers/Charts - Slicer Wiki View original

  Is this image relevant?

1 of 2

Top images from around the web for Categorical and Nominal Data

• 

  graphics - Good Ways to Visualize Longitudinal Categorical Data in R - Stack Overflow View original

  Is this image relevant?

• 

  Documentation/4.1/Developers/Charts - Slicer Wiki View original

  Is this image relevant?

• 

  graphics - Good Ways to Visualize Longitudinal Categorical Data in R - Stack Overflow View original

  Is this image relevant?

• 

  Documentation/4.1/Developers/Charts - Slicer Wiki View original

  Is this image relevant?

1 of 2

• Categorical data consists of values that can be divided into groups or categories (colors, types of cars, gender)
• Nominal data is a type of categorical data where the categories have no inherent order or ranking
  • Values are mutually exclusive and cannot be logically ordered
  • Assigning numbers to nominal data is arbitrary and does not imply order (jersey numbers, postal codes)

Ordinal Data

• Ordinal data is a type of categorical data where the categories have a natural order or ranking
  • Values can be logically ordered based on a scale or hierarchy (small, medium, large)
  • Differences between categories are not precisely measurable or consistent (rankings, survey responses)

Quantitative Data

• Quantitative data consists of numerical values that represent quantities or measurements
  • Values can be counted, measured, or calculated using mathematical operations
  • Can be further classified as discrete or continuous data
• Discrete data can only take on specific, distinct values often represented as whole numbers (number of children, votes cast)
• Continuous data can take on any value within a range and can be measured to various levels of precision (height, temperature)

Data Characteristics

Properties of Discrete and Continuous Data

• Discrete data often results from counting and has a finite number of possible values
  • Represented graphically with bar charts or pie charts
  • Measures of central tendency for discrete data include mode and median
• Continuous data results from measuring and has an infinite number of possible values within a range
  • Represented graphically with histograms or box plots
  • Measures of central tendency for continuous data include mean, median, and mode

Implications for Data Analysis

• Understanding whether data is discrete or continuous informs appropriate visualization and analysis techniques
  • Discrete data should not be displayed with line graphs implying intermediate values
  • Continuous data can be grouped into intervals or bins for analysis (age groups, income brackets)

Data Organization

Scales of Measurement

• Scales of measurement define the nature of information within the values assigned to variables
  • Nominal scale: categories with no inherent order (eye color, country of birth)
  • Ordinal scale: categories with a natural order but inconsistent differences (letter grades, customer satisfaction)
  • Interval scale: numerical values with consistent intervals but no true zero (temperature, dates)
  • Ratio scale: numerical values with consistent intervals and a true zero (height, income)

Data Classification

• Data can be classified based on its scale of measurement to determine appropriate analysis methods
  • Nominal and ordinal data are often classified as categorical or qualitative data
  • Interval and ratio data are often classified as quantitative or numerical data
• Classifying data helps ensure valid comparisons and conclusions are drawn during analysis
  • Categorical data should be summarized using frequencies, proportions, or percentages
  • Quantitative data can be summarized using measures of central tendency and dispersion (mean, standard deviation)