Skill: Distinguish discrete and continuous data

Discrete data are values you count. They are separate values, usually whole numbers, such as $(0,1,2,3)$.

Continuous data are values you measure. They can take any value within a range, including decimals, such as $(150.4\text{ cm})$ or $(12.73\text{ s})$.

A useful question is:

Is this quantity counted, or is it measured?

Worked example

A teacher records two pieces of information about each student:

1. The number of pets the student owns
2. The student’s height

Step 1: Examine the number of pets

Pets are counted. A student might have $(0,1,2,)$ or $3$ pets, but not $(2.5)$ pets.

Therefore, the number of pets is discrete data.

Step 2: Examine the student’s height

Height is measured. A student’s height could be $(150\text{ cm})$, $(150.5\text{ cm})$, or $(150.53\text{ cm})$.

Therefore, height is continuous data.

Even if the teacher records height only to the nearest centimetre, such as $(151\text{ cm})$, height is still continuous because it was produced by measurement.

Remember

• Counted values $\rightarrow$ discrete
• Measured values $\rightarrow$ continuous
• Rounding a measurement does not make it discrete.