Continuous Variable: How it is Different from Discrete Variable

A numerical variable is said to be a continuous variable if it can take an infinite number of real values within a given interval or range. This article will discuss different types of numerical variables: Continuous and Discrete variables, their types, and difference between continuous and discrete variable.

Variables in mathematics are just a symbol that can represent different values in an expression, and they are mainly classified into Categorical and Numerical Variables. 

• Categorical Variable is a variable that has two or more categories with no intrinsic ordering to the categories.
  • It is also known as Qualitative Variables.
  • Example: Sex, Age Group, Education Level
• Numerical Variable is a variable that can be either counted or measured.
  • It is also known as quantitative Variables.
  • Example: Height, Area, Distance, Time

Numerical Variables are further classified into discrete and Continuous Variables.

This article will discuss the concept of continuous and discrete variables.

Table of Content

• What is a Continuous Variable
• Types of Continuous Variable
  • Interval Variable
  • Ratio Variable
• What is a Discrete Variable
• Continuous Variable vs. Discrete Variable

What is a Continuous Variable?

A numerical variable is said to be a continuous variable if it can take an infinite number of real values within a given interval or range.

• It can take positive, negative, interns, fractional, and decimal values.
• Continuous data can change over time.
• Continuous data can be best shown on a line graph.
• It is generally measured on a scale such as height, weight, and temperature.
• It is ideal for inferential statistics. 

Example:

1. Height of people living in the Asian Continent
2. Weight of the students of a school
3. The temperature of a city in a year
4. Speed of airplane
5. Area of a house

Types of Continuous Variable:

Continuous Variables are broadly classified into:

• Interval Variable
• Ratio Variable

Interval Variable

The interval variable is a measurement variable that is used to define values measured along a scale, such that each point are equidistant from the other. 

• In simple terms, an interval variable is a variable where the difference between two points (or values) is meaningful. 
• It has no zero value.

Example: Temperature (when measured in Celsius and Fahrenheit scale), Time, IQ Test Score, etc.

Ratio Variable

• It is an extension of the Interval Variable, with the only difference being that the ratio variable already has zero.
• Unlike interval variables, here, you can perform multiplication and division operations.

Example: Temperature (when measured on Kelvin scale), Height, Weight, etc.

What is a Discrete Variable

Variables that can only take a finite number of values are called a discrete variables. 

• Variables whose values are obtained from counting are called Discrete Variables.
• All qualitative variables are discrete variables.

Example:

• Number of Wickets taken by a player
• Votes cast in an election
• Number of heads while tossing a coin 100 times

Difference between Continuous and Discrete Variable

Parameter	Continuous Variable	Discrete Variable
Definition	A numerical variable is said to be a continuous variable if it can assume infinite values in a given range.	Numerical Variable that can only assume a fixed number of distinct values.
Assumes	Any values between two values (or range).	Distinct or Separate Value.
Values	Obtained by Measuring	Obtained by counting
Change in Value	The value of continuous variables changes over time.	Values remain the same over a specific time interval.
Represented By	Connected Points	Isolated Points
Example	Weight/height of student in a school	Number of student in a school

Conclusion

Variables in mathematics or statistics are used to represent the values corresponding to its expression. Variables are broadly classified into Categorical and Numerical Variable. This article briefly discusses the numerical variable, its type with the help of examples. Later the article, also discusses the difference between Continuous and Discrete variables.

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