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###### Two-way Frequency Tables

Maths Applications (Year 12) - Bivariate Data Analysis

Aaron Gibson-John

# Bivariate Analysis

Bivariate analysis is a technique used in statistics to explore and understand the relationship between two variables in a dataset. This method is particularly useful for identifying patterns, trends, correlations, and potential causal relationships between two variables. By analysing two variables together, we can understand how changing one variable may lead to a change in another variable.

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Two-Way Frequency Tables

A two-way table is a tabular representation of the relationship between two categorical variables. Each variable is divided into categories or groups, and the table displays the frequency or count of occurrences for each combination of categories from both variables. Two-way tables are particularly useful for visualising and analysing how the distribution of one variable varies across different categories of another variable. They provide a clear overview of the joint distribution of the two categorical variables and allow researchers to identify any patterns or associations that might exist between them.

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Example: A person's sex and their ice-cream Preference

Suppose we have conducted a survey among a group of people to understand their ice-cream preferences based on the different sexes. The survey collected data on two categorical variables: "Sex" (with categories: Male, Female) and "Preferred Ice-cream Flavour" (with categories: Vanilla, Chocolate, Strawberry).

Here's the raw data from the survey:

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Based on this data, we can create a two-way frequency table to summarise the relationship between sex and preferred ice-cream flavour:

In this two-way table:

• The rows represent the different sexes, and the columns represent the various preferences for ice-cream flavour

• The numbers in each cell represent the number of respondents falling into the respective sex and ice-cream preference categories.

From this table, we can observe a few patterns:

• More males prefer chocolate ice-cream compared to other products.

• Vanilla and Strawberry flavours have roughly equal preference across genders.

• Females have a slightly higher preference for chocolate ice-cream compared to males.

This type of analysis helps us gain insights into how product preferences vary based on different criteria and allows marketers or researchers to tailor their strategies accordingly.

# Two-way Frequency Table | Elucidate video

In this video, Bhakti explains the fundamentals of two-way frequency table and breaks down how to solve a common two-way table question.

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