Displaying Two-Categorical Variables Part 2

What is a side-by-side bar graph used for?

• Displaying frequencies of one categorical variable

• Comparing the distributions of two categorical variables

• Showing trends over time

• Summarizing numerical data

In a segmented bar graph, how is the data represented?

• Each category has a separate bar

• Each bar is divided into segments representing categories of another variable

• Data is shown as a line graph

• Only totals are represented

What is a mosaic plot?

• A graphical representation that uses colors to show frequencies

• A bar graph that displays only totals

• A graphical display that shows the relative sizes of categories based on frequencies

• A scatter plot for two numerical variables

When two categorical variables are independent, what is true about their relationship?

• The variables influence each other

• The distribution of one variable does not affect the distribution of the other

• There is a perfect correlation

• They cannot be displayed on the same graph

Which of the following indicates that two variables are associated?

• The joint relative frequencies are equal across categories

• There is a noticeable pattern in the distributions

• The total counts are the same

• The variables have the same marginal distribution

In a side-by-side bar graph, what does each bar represent?

• A single variable's total frequency

• The frequency of one category compared across different groups

• The overall data set

• The average of two variables

How can you determine if two variables are independent using a contingency table?

• By checking if the total frequencies are equal

• By comparing joint frequencies with the product of marginal frequencies

• By observing the colors of the bars

• By summing all frequencies

What does a segmented bar graph visually illustrate?

• Total counts for each category

• The proportion of each category within a variable

• The joint frequencies of two categorical variables

• Marginal frequencies only

What key feature distinguishes a mosaic plot from other graphical displays?

• It displays only numerical data

• It represents frequencies using area sizes of rectangles

• It uses line segments to connect points

• It shows only independent variables

If the segmented bar for one variable shows significantly different segment sizes than another, what can be inferred?

• The variables are independent

• The variables are associated

• The data is incorrect

• The totals are the same