Distinguish discrete and continuous data

Detailed Explanation: Distinguish discrete and continuous data

Discrete data come from counting. The possible values are separate and countable, such as $(0,1,2,3,\ldots)$.

Continuous data come from measuring. The quantity can take any value within an interval, depending on how precisely it is measured.

To decide:

1. Identify what the numbers represent.
2. Ask whether you are counting separate objects or events.
3. If so, the data are discrete.
4. If you are measuring an amount such as length, time, mass, or temperature, the data are continuous.
5. Do not decide only by looking at whether the recorded numbers are whole numbers. Measurements are often rounded.

Worked example

A student measures plants and records:

• the number of leaves on each plant;
• the height of each plant, recorded to the nearest centimetre.

Classify each type of data.

Step 1: Examine the number of leaves.

The student is counting separate leaves. A plant might have $8$ leaves or $9$ leaves, but not $(8.4)$ leaves.

Therefore, the number of leaves is discrete data.

Step 2: Examine the plant height.

The student is measuring length. A plant recorded as $(18)$ cm could have an actual height anywhere from $(17.5)$ cm up to, but not including, $(18.5)$ cm when rounded to the nearest centimetre. More precise equipment could record values such as $(18.27)$ cm.

Therefore, plant height is continuous data.

Answer:

• Number of leaves: discrete, because it is counted.
• Plant height: continuous, because it is measured and can take any value in an interval, even though the recorded values are rounded to whole centimetres.