Types of Data (VCE SSCE General Mathematics): Revision Notes

Types of Data

Understanding different types of data is fundamental to statistics. When you collect information through surveys or experiments, the nature of that information determines how you can analyse and interpret it. Let's explore the main categories of data and how to classify them correctly.

Variables and data

When we conduct surveys or experiments, we collect information that varies between individuals or observations. Each characteristic we measure is called a variable. For example, if you survey students about their height, weight, age, and study preferences, each of these characteristics is a separate variable.

The actual values we collect for these variables are called data. For instance, if one student is $173$ cm tall, weighs $57$ kg, and is $18$ years old, these specific numbers are the data points.

Here's an example dataset from a student survey:

This table shows six different variables (height, weight, age, study mode, fitness level, and pulse rate) collected from eight students. Notice how each variable produces different types of information.

Types of variables

All variables can be classified into two main categories: categorical and numerical. Understanding which type you're working with is crucial because it determines what kind of analysis you can perform.

Categorical variables

Categorical variables describe qualities or attributes rather than quantities. They sort individuals into different groups or categories. For example, a person's eye colour, their preferred study mode, or their fitness level are all categorical variables.

When you collect data from a categorical variable, you're essentially labelling each individual with a category name. In our student survey example, Study mode is categorical because it places students into either the "on-campus" or "online" group.

Categorical variables come in two distinct types:

Nominal variables

Nominal variables simply name or label categories without any inherent order. The word "nominal" comes from the Latin word for "name," which helps you remember its meaning.

Think of study mode (on-campus versus online) as an example. There's no logical way to say one category comes "before" or "after" the other—they're just different options with no ranking. Other examples include eye colour, favourite sport, or country of birth.

Ordinal variables

Ordinal variables go one step further than nominal variables. Not only do they name categories, but they also allow you to arrange those categories in a logical order. The word "ordinal" relates to "order," which is your clue to its meaning.

Consider the fitness level variable in our survey, which uses the scale: $1$ = high, $2$ = medium, $3$ = low. These numbers don't represent actual measurements; instead, they rank students' fitness levels from high to low. You can clearly order these categories: high fitness is better than medium, which is better than low.

Numerical variables

Numerical variables represent quantities that arise from counting or measuring. These variables produce data that are actual numbers with mathematical meaning. For instance, a height of $179$ cm or a pulse rate of $82$ beats per minute are numerical values that tell you "how much" or "how many."

The key feature of numerical variables is that you can perform arithmetic operations on them. You can calculate averages, find differences, and compare values in meaningful ways.

Numerical variables are classified into two types:

Discrete variables

Discrete variables can only take specific, countable values. Typically, these are whole numbers like $0, 1, 2, 3, 4, \ldots$ and often arise from counting situations.

When someone asks "How many?" the answer usually involves a discrete variable. For example:

• How many mobile phones are in your house?
• How many students are in your class?
• How many goals were scored in a football match?

You cannot have $2.7$ mobile phones or $15.3$ students—discrete variables only take distinct, separate values. Even if you count a very large number of items, each count is a specific whole number.

Continuous variables

Continuous variables can take any value within a range and are associated with measuring rather than counting. Theoretically, continuous variables have infinite possible values, even though our measuring instruments limit how precisely we can record them.

When someone asks "How much?" the answer typically involves a continuous variable. For example:

• How much does a person weigh?
• How much time did it take to complete a task?
• How much rainfall was recorded?

Consider height: even though we might record someone's height as $179$ cm, their actual height could be any value between $178.5$ cm and $179.5$ cm. We round to $179$ cm because that's as precise as our measuring device allows, but the true value is somewhere in that continuous range.

Distinguishing between numerical and categorical data

Sometimes it's not immediately obvious whether a variable is numerical or categorical. Understanding the distinction is crucial for proper analysis. Here are two helpful strategies to make the classification:

Worked example: Classifying data types

Let's practice classifying different types of data. For each scenario below, determine whether the data is nominal, ordinal, discrete, or continuous.