Categorical vs Quantitative Data Cheat Sheet

Key Facts

• Categorical data place individuals into groups or labels, such as eye color, favorite sport, or type of pet.
• Quantitative data are numerical measurements or counts where arithmetic is meaningful, such as height, time, age, or number of siblings.
• A frequency is the count in a category, and the total sample size is $n = \sum f$.
• Relative frequency is found with $\text{relative frequency} = \frac{\text{category frequency}}{\text{total frequency}}$.
• A percent frequency is found with $\text{percent} = \frac{\text{part}}{\text{whole}} \times 100\%$.
• The mean of quantitative data is $\bar{x} = \frac{x_1 + x_2 + \cdots + x_n}{n}$.
• The range of quantitative data is $\text{range} = \text{maximum} - \text{minimum}$.
• Use bar graphs for categorical data and dot plots, histograms, or box plots for quantitative data.

Vocabulary

Categorical Data

Data that describe qualities, groups, names, or labels rather than measurements.

Quantitative Data

Data made of numbers that represent counts or measurements where arithmetic is meaningful.

Variable

A characteristic being recorded or measured for each individual in a data set.

Frequency

The number of times a value or category appears in a data set.

Relative Frequency

The fraction or proportion of the total data that belongs to a category.

Distribution

The pattern of values in a data set, including where values cluster and how they spread out.