Distinguish categorical, discrete, and continuous data

Detailed Explanation: Distinguish categorical, discrete, and continuous data

To classify a variable, ask what its values mean and how they are obtained.

1. Categorical data are labels or groups. They may be:

   • Unordered, such as eye colour: brown, blue, or green.
   • Ordered, such as satisfaction: dissatisfied, neutral, or satisfied.

   Even if categories are given numerical codes, they are still categorical. For example, coding eye colours as $1=$ brown, $2=$ blue, and $3=$ green does not make eye colour numerical data.

2. Discrete numerical data are numbers produced by counting. The possible values are separate, such as $0,1,2,3,\ldots$. You cannot usually have a fraction of the object being counted.

3. Continuous numerical data are measurements. In principle, a measurement can have any value within an interval, even if it is rounded when recorded.

Worked example

A school surveys students and records:

• their method of travel to school;
• the number of pets they own;
• their travel time to school, recorded to the nearest minute.

Classify each variable.

Step 1: Method of travel

Possible values might be bus, car, bicycle, or walking. These are labels, not amounts that can be added or measured.

Therefore, method of travel is categorical data.

Step 2: Number of pets

Possible values are counts such as $0,1,2,3,\ldots$. A student can have $2$ pets or $3$ pets, but not usually $2.5$ pets.

Therefore, number of pets is discrete numerical data.

Step 3: Travel time

Travel time is measured. A student’s actual time could be $12.4$ minutes, $12.43$ minutes, or another value in an interval. Recording it as $12$ minutes is only rounding the measurement.

Therefore, travel time is continuous numerical data.

So the classifications are:

When deciding, remember: labels are categorical, counts are discrete, and measurements are continuous—even when measurements are rounded.