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FM Categorical Data

2.1 Response and Explanatory Variables

Explanatory Variable

  • The explanatory variable (EV) is the variable used to explain or predict another variable (the response variable).
  • By convention, the explanatory variable is plotted along the x-axis of a graph, if it is numerical.

Response Variable

  • The response variable (RV) is the variable which is explained or predicted by the explanatory variable.
  • By convention, the response variable is plotted along the y-axis of a graph, if it is numerical.

Note: both explanatory and response variables can be either categorical or numerical variables.

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1.3 Statistical Analysis of Categorical Distributions

Answering Statistical Questions on Categorical Distributions


  • The mode of categorical data refers to the category with the highest frequency.

Note: the mode of a categorical distribution is also known as the modal category, or dominant category


Given the bar chart:

Bar Chart for Categorical Data

Red has the highest frequency and so it is the modal category.

Guidelines to analysing categorical distributions

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1.2 Displaying Distributions of Categorical Data

Visualising Categorical Data


  • The number of times a particular value or category occurs is known as the frequency. This is often used as the basis for displaying and analysing categorical data.


In the following dataset of colours:

Red Red Blue Red

The frequency of each colour is:

Red: 3

Blue: 1


  • The proportion of the total data points which belong to a particular group is known as the percentage.
  • This can be calculated using the formula:
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1.1 Overview of Data Types

Categorical Data

  • Data which is sorted into groups is considered categorical data

Nominal Data

      • Categorical data with no hierarchy (i.e. one category is not “greater than” another) is considered nominal data


Eye colour can be considered a nominal data type as the data (each person’s eye colour) can be placed into groups and there is no hierarchy

Ordinal Data

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