Skill: Distinguish discrete and continuous data

Data can be classified by asking what the variable represents:

• Discrete data are counts. They have separate, countable values, such as $(0,1,2,3,\ldots)$.
• Continuous data come from measuring. They can take any value within a range, even if the recorded value is rounded.

Worked example

A teacher records the following information about students:

1. The number of pets each student owns
2. Each student’s height, recorded to the nearest centimetre

Classify each variable as discrete or continuous.

Step 1: Identify what is being recorded

• “Number of pets” is a count.
• “Height” is a measurement.

Step 2: Decide whether values are countable or measurable

• The number of pets can be $(0,1,2,3,\ldots)$. You cannot have $(2.5)$ pets in this count, so it is discrete data.
• Height could be $(160.2\text{ cm})$, $(160.25\text{ cm})$, or another value between two measurements. Even though it is recorded to the nearest centimetre, it is still continuous data.

Answer

• Number of pets: discrete
• Height: continuous

Remember: whole-number recordings do not automatically mean the data are discrete. Ask whether the variable is being counted or measured.