Chapter 1 Types of variables

Before we begin learning how to make sense of data via methods such as frequency tables, charts, and statistical summary measures, let's first consider two main types of variables: categorical (qualitative) variables, and numerical (quantitative) variables. Both of these variable types have two different sub-types:

Categorical (qualitative) Variable

A variable that is separated into groups. Categorical variables can be either:

• Nominal: Where the groups are characterised by names, labels or categories. For example, eye colour (blue, brown, green, etc.), car brand (Hyundai, Toyota, Holden, etc.), or state (VIC, NSW, SA, etc.).
• Ordinal: Where the groups can be arranged into a specific order. For example, how much a person smokes (never, occasional, regular, heavy), or level of exercise (none, some, frequent).

Numerical (quantitative) Variable

A numerical variable is one that represents counts or measurements. The two types of numerical variables we will be looking at are:

• Discrete: Where the set of all possible values is countable. For example, the number of heartbeats per minute, or the number of heads observed when flipping a coin five times.
• Continuous: Where the variable can take an infinite number of values within a certain range. For example, height, weight or age.

Test your knowledge

1. The number of children in your family would be considered what type of variable? Numerical > Continuous Categorical > Ordinal Numerical > Discrete Categorical > Nominal
2. Your grade in this subject (A, B, C, D, N) would be considered what type of variable? Numerical > Continuous Categorical > Ordinal Numerical > Discrete Categorical > Nominal
3. Your height would be considered what type of variable? Numerical > Continuous Categorical > Ordinal Numerical > Discrete Categorical > Nominal
4. Descriptive statistics ... involves drawing conclusions from data involves collecting, describing, and analysing data, and sometimes drawing conclusions from data involves summarising and displaying data via graphical and numerical means
5. Inferential statistics ... involves drawing conclusions from data involves collecting, describing, and analysing data, and sometimes drawing conclusions from data involves summarising and displaying data via graphical and numerical means
6. Place the following words into the correct boxes: "population", "inferences", "sample"

Normally, we use the data available to us in the to make about the .

1. Numerical > Discrete
2. Categorical > Ordinal
3. Numerical > Continuous
4. Descriptive statistics involves summarising and displaying data via graphical and numerical means.
5. Inferential statistics involves drawing conclusions from data.
6. Normally, we use the data available to us in the sample to make inferences about the population.

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These notes have been prepared by Amanda J. Shaker. The copyright for the material in these notes resides with the author named above, with the Department of Mathematics and Statistics and with La Trobe University. Copyright in this work is vested in La Trobe University including all La Trobe University branding and naming. Unless otherwise stated, material within this work is licensed under a Creative Commons Attribution-Non Commercial-Non Derivatives License CC BY-NC-ND