2. Exploring Data

a. Categorical Data

Yurk

Comic Characters Dataset

15,516 comic characters from DC and Marvel comics
Key variables:
- name: Character name
- identity (id): Personal identity status (secret, public, no dual)
- alignment (align): Good, bad, neutral, etc.

We can summarize a categorical variable using a frequency table:

Recall from 1a: A categorical variable takes values that are labels — categories each case falls into.

A summary statistic is a single number that summarizes a sample.

For categorical data, the common summary statistics are:

Means, medians, and standard deviations are summary statistics for numerical data — that’s the focus of 2b.

Proportion: What fraction of comic characters have a secret identity?

\text{Proportion} = \frac{\text{Count}}{\text{Total}} = \frac{7,928}{15,516} = 0.511

Percentage: What percent of comic characters have a secret identity?

\text{Percentage} = \text{Proportion} \times 100 = 0.511 \times 100 = 51.1\%

Adding proportions to the table reveals patterns more clearly than raw counts:

Counts tell you how many. Proportions tell you how much — the share each category takes of the whole.

Frequency table for comic character alignment:

Compute each — advance for answers:

Question	Answer
Proportion of Good characters	0.39
Percentage of Bad characters	46.1%
Proportion that are not Neutral	0.851

We can visualize categorical data using a bar plot:

Bar length encodes the count — the visual makes it easy to compare categories at a glance.

Introduction to Modern Statistics (2e) textbook by Mine Çetinkaya-Rundel and Johanna Hardin
Sections 1.1, 4.1