## Table of Contents

- What is a Continuous Variable?
- Discrete Variable
- Continuous Quantitative Variable
- Continuous Variable Examples
- Lesson Summary

- FAQs
- Activities

## Identifying Continuous Variables: Additional Practice

In the following problems, students will identify if a variable is continuous, or not, and explain the reasoning behind the identification.

## Problems

**1.** Out of the following, which one is NOT a continuous variable. Why not?

- Length of hair
- Number of children
- Weight of a box
- Height of a tree

**2.** Out of the following, which is a continuous variable? Why?

- Number of pets
- Color of shirt
- Temperature
- Outcomes from flipping a coin

**3.** A student was giving a presentation on continuous variables in statistics class and received a failing grade because they described the number of people in a household as a continuous variable, using the statistic that the mean household size is 4.2 people. Explain why the number of people in a household is not continuous, even though the mean contains a decimal.

### Solutions

**1.** The number of children is *not* a continuous variable. It is not continuous because we cannot have a fraction of a child - only whole numbers.

**2.** Temperature is a continuous variable because it can take on any value in an interval of values - we can have decimals in a temperature measurement.

**3.** The number of people in a household is *not* continuous because you cannot have a fraction of a person - only whole people. This does not mean that the mean household size cannot have a fraction or decimal, just that each individual household can only have a whole number of people. For example, the mean household size for a sample of households of size 3, 4, 2, and 5 is (3 + 4 + 2 + 5) / 4 = 14 / 4 = 3.5, even though we cannot have a fraction of a person.

#### How do you know if a variable is continuous?

At a first glance, any variable that can be measured in decimals or fractions can be considered continuous. On the other hand, variables that can only be presented as whole numbers are called discrete.

#### What are two examples of continuous variables?

Two examples of continuous variables are:

1. Body weight (e.g., 34.879 Kg)

2. Height (e.g.: 1.7589 m)

In both examples the value could present an unlimited number of digits after the decimal point.

#### What are continuous variables in math?

In mathematics, a continuous variable can assume a value within a range that includes infinite possible values. The are commonly presented as decimals or fractions.

#### What is the difference between continuous and discrete variables?

Continuous variable can assume an infinite number of values within a range. They are usually represented by decimals or fractions. Discrete variables are whole number values that represent units that cannot be presented as decimals or fractions.

#### What is considered a continuous variable?

A continuous variable is any value that can be measured as decimals or fractions. These are infinitely situated between two values of reference. For example, there are infinite values between 1 and 2.