Range Definition

It is a Statistical term used in Mathematics in two different sections. Let us show you what is Range in those dimensions.

  • Range is defined as the difference between the smallest and largest numbers of a given set.
  • Range is defined as the set of answers you will get for a function by inserting a particular set of domains.

These are the definition of Range in Mathematics. You have to understand it properly in a particular dimension when you are learning or solving questions related to this term.


You can read about Statistics and Domain of a function here.


How to find Range?

As mentioned above, it has two different definitions in different conditions in Mathematics and Statistics. Let us show you how to find Range in both conditions one by one.

Range between two Numbers

If you have a set of numbers, you can find the Range of that set by following a simple formula. You only have to subtract the smallest number from the largest one to find the difference. Here is the general formula for this purpose.

Range = Largest Value – Smallest Value

Steps to find Range

  • Write the set on a page
  • Extract the smallest value
  • Find the largest value
  • Put those values in the above formula to solve the problem

Example 1:

Find the Range of the following set:

{2, 3, 4, 5, 9, 10, 34, 23, 67, 78, 90, 89, 25}


Largest Value = 90
Smallest Value = 2
Range = 90 - 2
Range = 88

[Pro Tip: Keep in mind that the largest number doesn’t mean the last entry of the set. It means the greatest value of the given set]

Range of a Function

In Statistics, it is common to deal with different functions for which you are given a particular domain. It means you are given some values to check the validity of the function by using those values.

In this case, Range is the collection of numbers that come out by putting the valid Domain entries in that function.

Steps to find Range

  • Write a function on the page
  • Note all the Domain values
  • Put all of those values one by one in the function
  • Keep writing the output in a particular set
  • The set of all values at the end will be termed as the Range of that function


Range of a function can also be shown in Venn Diagram which you can read here in detail.


What is the relationship between Domain and Range?

A domain is the input while the Range is the output of the same function.

Can we find the Range of a set having 100 elements (numbers)?

Yes, you can find a range of any set without checking the number of elements. You only have to find the smallest and largest values of that set.

What is the significance of the Range?

It has deep roots in Mathematics and Statistics. Along with this, it is important to find this term in many practical fields like Engineering to solve many critical problems.