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.

Frequency Tables

We can summarize a categorical variable using a frequency table:

identity count
No Dual 1,511
Public 6,068
Secret 7,928
Unknown 9
Total 15,516

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

Summary Statistics

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

For categorical data, the common summary statistics are:

  • count — number of cases in each category
  • proportion — count ÷ total
  • percentage — proportion × 100

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

Proportions and Percentages

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?

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

Proportions Reveal Patterns

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

identity count proportion
No Dual 1,511 0.097
Public 6,068 0.391
Secret 7,928 0.511
Unknown 9 0.001
Total 15,516 1.000

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

Proportions

Frequency table for comic character alignment:

alignment count
Bad 7,146
Good 6,052
Neutral 2,316
Reformed Criminals 2
Total 15,516

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

Bar Plots

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.

References