## Discrete Variable

**Definition:**

Discrete variable is a mathematical term used to describe a variable that can only take on a finite number of values. In other words, it is not continuous. Discrete variables are often used in statistics and probability theory.

### Discrete Variable in Research

Discrete variable in research is a variable that can take on a limited number of values. Discrete variables are often used to represent categorical data, such as gender, ethnicity, and zip codes.

### Examples of Discrete Variable

Examples of Discrete Variables would be:

- The number of people in a room
- The number of classes you have taken
- Whether it is raining or not
- The number of Students in Class
- The number of cars in the parking
- The number of people who voted for a particular candidate
- Coins in your pocket
- The points scored in a football game
- Categorical variables such as gender (male/female) or hair color (blond/brown/red/etc.) are also considered to be discrete.
- ETC….

### Types of Discrete Variable

There are four Types of Discrete Variable:

- Dichotomous variables
- Categorical variables (or nominal variables)
- Ordinal variables
- Nominal variables

#### Dichotomous variables

Dichotomous variables are those that can be divided into two groups. The groups can be based on anything, but they are usually either on or off, true or false, positive or negative. Dichotomous variables are important in research because they allow for clear and concise results. They also allow for easy comparison between two groups.

#### Categorical variables

Categorical variables are a type of data that can be divided into groups. They are often used to group data by characteristics such as race, gender, or income level..

#### Ordinal variables

An ordinal variable is a type of data that is assigned a rank or order. Ordinal variables are often used in surveys and questionnaires to collect data about people’s preferences and opinions.

#### Nominal variables

Nominal variables are those that can be classified into non-numeric categories. Examples of nominal variables include gender, religious affiliation, and country of origin. Nominal variables are often used in social science research to measure factors such as beliefs, attitudes, and values.

### When to use Discrete Variable

Discrete variables are often used when modeling data that represents a count or frequency. For example, if you were interested in modeling the number of people who visit a certain website each day, you would use a discrete variable. Discrete variables are also used when data is categorical in nature. For example, if you wanted to model the number of people who prefer one type of food over another, you would use a discrete variable.

### Purpose of Discrete Variable

There are many purposes for using discrete variables in research. For example, they can be used to measure the frequency of something occurring, or to track the number of times something happens. They can also be used to look at how two or more things are related to each other. Discrete variables are an important tool for researchers because they allow us to measure and understand the world around us in a more precise way.

#### Advantages of Discrete Variable

There are several advantages of using discrete variables:

- Discrete variables are often more realistic than continuous variables. For example, when modeling the number of people in a room, it is more realistic to assume that there can only be a certain number of people (a discrete variable) than to assume that there can be any number of people (a continuous variable).
- They are often easier to work with mathematically than continuous variables. This is because it is often easier to calculate with specific values than with ranges of values.
- It can sometimes give more accurate results than continuous variables.

#### Limitations of Discrete Variable

There are some limitations of Discrete Variables:

- Discrete variables is that they can only represent a finite set of values. This means that if you want to represent a continuous quantity, such as time or temperature, you will need to use a different type of variable.
- They can sometimes be hard to work with mathematically. This is because many mathematical operations, such as differentiation and integration, require the use of continuous variables.
- Discrete variables can also be less accurate than continuous variables when measuring certain quantities. This is because they can only take on a limited number of values, which means that they may not be able to accurately represent all the variation in a quantity.