Skill: Distinguish discrete and continuous data

Data can be classified by asking how the values are obtained:

• Discrete data are counted. They have separate, countable values, usually whole numbers.
• Continuous data are measured. They can take any value within a range, including decimals.

Worked example

A teacher records the following information about students:

1. The number of pets each student owns
2. Each student’s height
3. The number of goals each student scored in a game
4. Each student’s running time

Step 1: Ask whether the quantity is counted or measured.

• Pets and goals are counted.
• Height and running time are measured.

Step 2: Classify each quantity.

• The number of pets is discrete data. A student can have $(0,1,2,3,\ldots)$ pets, but not $(2.5)$ pets.
• Height is continuous data because it can be any measurement in a range, such as $(150\text{ cm})$, $(150.5\text{ cm})$, or $(150.52\text{ cm})$.
• The number of goals is discrete data because goals are counted in separate whole numbers.
• Running time is continuous data because time is measured and can include values such as $(12.4)$ seconds or $(12.43)$ seconds.

Important: Rounding does not change the type of data. For example, if a student’s height is recorded as $(151\text{ cm})$ after rounding, height is still continuous data because it was originally measured.