Types of Data

Why Data Classification Matters

Before analyzing any dataset, you must understand what type of data you’re working with. The type of data determines:

• Which statistical methods are appropriate
• How to visualize the data effectively
• What summary statistics make sense
• Which hypothesis tests you can use

Using the wrong method for your data type can lead to meaningless or misleading results.

The Big Picture: Categorical vs Numerical

All data falls into two fundamental categories:

Type	Description	Examples
Categorical	Data that represents groups or categories	Gender, color, yes/no responses
Numerical	Data that represents measurable quantities	Height, temperature, count of items

Let’s explore each in detail.

Categorical (Qualitative) Data

Categorical data describes qualities or characteristics. It places observations into groups or categories.

Types of Categorical Data

1. Nominal Data

Categories with no natural order or ranking.

Key characteristics:

• Categories are mutually exclusive
• No category is “greater” or “less” than another
• Can only count frequencies
• Mode is the only meaningful measure of central tendency

2. Ordinal Data

Categories with a meaningful order, but differences between categories aren’t equal.

Key characteristics:

• Categories have a logical order
• Distances between categories may not be equal
• Can use median and mode, but mean is problematic
• Can say “greater than” but not “how much greater”

Numerical (Quantitative) Data

Numerical data represents quantities that can be measured or counted. Mathematical operations are meaningful.

Types of Numerical Data

1. Discrete Data

Data that can only take specific, countable values. Usually integers (whole numbers).

Key characteristics:

• Countable, finite values in any range
• Often integers, but not always
• Gaps exist between possible values
• “How many?” questions

2. Continuous Data

Data that can take any value within a range. Infinitely many possible values.

Key characteristics:

• Infinitely many possible values between any two points
• Limited only by measurement precision
• No gaps between possible values
• “How much?” questions

The Four Scales of Measurement

Statistician Stanley Stevens proposed four levels of measurement, from least to most informative:

1. Nominal Scale

• Properties: Categories with no order
• Operations: Equality (=, ≠)
• Central tendency: Mode only
• Examples: Gender, nationality, eye color

2. Ordinal Scale

• Properties: Categories with order
• Operations: Equality and Order comparisons
• Central tendency: Mode, Median
• Examples: Rankings, education level, satisfaction ratings

3. Interval Scale

• Properties: Ordered with equal intervals, but no true zero
• Operations: Equality + Order + Addition/Subtraction
• Central tendency: Mode, Median, Mean
• Examples: Temperature (°C, °F), calendar years, IQ scores

4. Ratio Scale

• Properties: Ordered, equal intervals, AND a true zero point
• Operations: All mathematical operations
• Central tendency: Mode, Median, Mean, Geometric Mean
• Examples: Height, weight, age, income, distance

Comparison Chart

Property	Nominal	Ordinal	Interval	Ratio
Categories	✓	✓	✓	✓
Meaningful order	✗	✓	✓	✓
Equal intervals	✗	✗	✓	✓
True zero	✗	✗	✗	✓
Example	Blood type	Pain level	Temperature (°C)	Height

Identifying Data Types: Practice Framework

When classifying data, ask these questions in order:

1. Can you do arithmetic with it meaningfully?
   ├── NO → Categorical
   │         ├── Is there a natural order? 
   │         │   ├── NO → Nominal
   │         │   └── YES → Ordinal
   └── YES → Numerical
             ├── Can it take any value in a range?
             │   ├── NO → Discrete
             │   └── YES → Continuous
             └── Is there a true zero point?
                 ├── NO → Interval
                 └── YES → Ratio

Common Pitfalls

1. Numbers Aren’t Always Numerical

Just because data contains digits doesn’t make it numerical:

• Phone numbers → Nominal
• ZIP codes → Nominal
• Jersey numbers → Nominal
• Social Security numbers → Nominal

2. Coded Categories

Sometimes categories are coded as numbers for convenience:

• Gender: 1 = Male, 2 = Female → Still Nominal
• Education: 1 = HS, 2 = Bachelor’s, 3 = Master’s → Still Ordinal

3. Discrete Can Look Continuous

Data with many discrete values (like income in dollars) can be treated as continuous for practical purposes.

4. Continuous Data is Always Recorded as Discrete

Due to measurement precision, we record continuous data with finite decimal places, but the underlying variable is still continuous.

Why This Matters for Analysis

Data Type	Appropriate Visualizations	Summary Statistics	Common Tests
Nominal	Bar chart, Pie chart	Mode, Frequencies	Chi-square
Ordinal	Bar chart, Box plot	Median, IQR	Mann-Whitney, Wilcoxon
Interval/Ratio (Discrete)	Histogram, Bar chart	Mean, SD, Median	t-test, ANOVA
Interval/Ratio (Continuous)	Histogram, Box plot, Scatter plot	Mean, SD, Median	t-test, ANOVA, Regression

Real-World Application

Summary

In this lesson, you learned:

• Categorical data represents groups (nominal = unordered, ordinal = ordered)
• Numerical data represents quantities (discrete = countable, continuous = measurable)
• The four scales of measurement: Nominal < Ordinal < Interval < Ratio
• True zero distinguishes interval from ratio scales
• Data type determines which statistical methods are appropriate
• Numbers aren’t always numerical—context matters!

Practice Problems

Classify each variable as Nominal, Ordinal, Discrete, or Continuous:

1. Satisfaction score (Very Unsatisfied to Very Satisfied)
2. Number of pets owned
3. Hair color
4. Body temperature in Fahrenheit
5. Class rank (1st, 2nd, 3rd, …)
6. Salary in dollars
7. Favorite ice cream flavor
8. Test score (0-100)

Click to see answers

1. Ordinal - Ordered categories
2. Discrete - Countable whole numbers
3. Nominal - Unordered categories
4. Continuous - Can take any value (but interval scale, not ratio)
5. Ordinal - Ordered but differences aren’t equal
6. Continuous - Can take any value (ratio scale)
7. Nominal - Unordered categories
8. Discrete - Finite set of values (could argue continuous if partial credit)

Next Steps

Now that you understand data types:

• Data Collection Methods - How to gather different types of data
• Measures of Central Tendency - Summarizing numerical data
• Data Visualization - Choosing the right charts for your data type