Wiki Page, Math 13 - Perez Sandbox : Module 12 - Introduction to Types of Quantitative Variables

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2026-01-17T21:15:15-08:00

In our previous discussion of probability distributions, we examined probability distributions for categorical variables (e.g. blood type) and quantitative variables (e.g. number of boreal owl eggs in a nest).

When the variable is quantitative, we described the probability distribution using shape, center and spread.

When the outcomes are quantitative, statisticians call the variable a random variable. They also distinguish between discrete quantitative variables and continuous quantitative variables.

Discrete quantitative variables (aka discrete random variables) have numeric values that can be listed and counted. Examples of discrete quantitative variables:

number of boreal owl eggs in a nest

number of times a college student changes her major

shoe size

Continuous quantitative variables (aka continuous random variables) have numeric values that cannot be listed and counted. Theoretically, we can measure a continuous variable to any desired accuracy. Examples of continuous quantitative variables:

weight

foot length

Why is shoe size a discrete quantitative variable but foot length is a continuous quantitative variable?

We view measurements as continuous even though the limitations of a ruler or a scale give discrete measurements. For example, imagine weighing yourself on a digital scale that gives weights to the nearest tenth of a pound. You will get measurements that are rounded to the nearest tenth, such as 152.3 lbs. Theoretically, we could measure your actual weight to any desired decimal place if we had a special scale, such as 152.345612555 or something like that. This is why we cannot list all of the variable values. This is not true with a discrete variable like shoe size.

A note about terminology:

When we discuss probability, we use the word random to mean that the outcomes are uncertain in the short run but have a regular distribution or predictable pattern in the long run. However, statisticians reserve the term random variable for quantitative variables. This can be a bit confusing because categorical variables can also describe random outcomes. We will just call them "quantitative" variables instead of "random" variables to avoid this confusion.

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