Types of Data

The Data Classification Tree

All data in statistics can be classified into two main branches:

Data
├── Categorical
│   ├── Nominal
│   └── Ordinal
└── Numerical
    ├── Discrete
    └── Continuous

Categorical Data

Categorical data represents qualities or characteristics — values fall into categories, not numbers.

Nominal Data

• Categories have no natural order
• Examples: eye colour (blue, brown, green), gender, country of birth, type of pet
• Displayed with: bar charts, pie charts

Ordinal Data

• Categories have a natural order but the gaps between categories are not measurable
• Examples: satisfaction rating (poor/fair/good/excellent), education level, competition placing (1st/2nd/3rd)
• Displayed with: bar charts (ordered)

KEY TAKEAWAY: Ordinal data has order but not equal spacing. You can say “good is better than fair” but not “good is twice as good as fair.”

Numerical Data

Numerical data represents quantities that can be measured or counted.

Discrete Data

• Can only take specific, separate values (usually whole numbers — you count them)
• Examples: number of children, number of cars sold, score on a test (out of 20)
• Displayed with: dot plots, stem-and-leaf, bar charts (with gaps)

Continuous Data

• Can take any value within a range (measured on a continuous scale)
• Examples: height, weight, temperature, time, distance
• Displayed with: histograms, box plots

Summary Table

Choosing the Right Display

The type of data determines which graphs are appropriate:

• Nominal/ordinal: bar chart, pie chart, frequency table
• Discrete: dot plot, stem-and-leaf, frequency table
• Continuous: histogram, boxplot, back-to-back stem plot

EXAM TIP: A common VCAA question asks you to identify the data type. Always look at whether it’s measured (continuous) or counted (discrete), and whether it’s a category or a number.

COMMON MISTAKE: Treating shoe size as continuous — it’s actually discrete (comes in whole/half sizes). Always think about whether values in between make sense.