# 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**.

**Note:**

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

**Table of Contents**

## 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}

**Solution:**

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**

**Note:**

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

### FAQ's

**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.