Representing a Categorical Variable with Graphs

Picturing categories

• A table of counts is fine, but a picture makes patterns jump out.
• For a categorical variable, the two workhorses are the bar chart 条形图 and the pie chart 饼图.
• Both show how individuals split across categories — bar charts by height, pie charts by slice.
• Choosing and reading them correctly is a core skill.

Bar charts

• A bar chart draws one bar per category, its height the frequency or relative frequency.
• Bars are separated (categories are distinct groups, not a continuous scale).
• The tallest bar is the most common category; comparing heights compares groups.
• Bars can be ordered any way — often tallest-to-shortest for clarity.

The same data as a bar chart and as a pie chart

Pie charts

• A pie chart shows each category as a slice of the whole circle.
• Slice size = that category's share (relative frequency) of the total.
• It's best when you care about parts of a whole and there are only a few categories.
• All slices add to $100\%$ — a pie always represents one complete group.

Comparing two categorical variables

• To compare a categorical variable across groups, use a side-by-side or segmented (stacked) bar chart.
• Side-by-side puts groups' bars next to each other; segmented stacks the categories within one bar per group.
• Look for an association 关联: do the category proportions differ between groups?
• If the proportions look the same across groups, there's little association.

Write from gaps between category bars

• A chart shows favourite sports as separate bars.
• The bars do not touch.