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# Quartile Calculator

Enter the numbers separated by commas in the quartile calculator and click calculate to find Q1, Q2, Q3, and IQR.

Table of Contents:

## Quartile Calculator

Quartile calculator is an online tool that can find:

- First Quartile (
**Lower**) - Median (
**2nd Quartile**) - Third Quartile (
**Upper**) - Interquartile Range (
**IQR**)

In this post, you will learn about quartiles and how to find them.

## Quartiles - Definition

**Quartiles **are three such points that divide a group into four equal parts. Each quartile accounts for a separate fourth part.

**First Quartile (Q1)**

It is the lower quartile which is the **25th **percentile of the group. It is the point that divides the group in a ratio of **1:3**.

**Second Quartile (Q2)**

It is the central quartile which is the **50th **percentile of the data. It is the point that divides the group in a ratio of **2:2**. It is also called the median.

**Third Quartile (Q3)**

It is the upper quartile which is the **75th **percentile of the group. It is the point that divides the group in a ratio of **3:1**.

**Note:** A group is divided into **100 **percentiles.

## Quartile Formulas

There is a general quartile formula that is adjusted according to the need for calculating a particular quartile. This formula is:

Where ’**J**’ is the number of quartiles i.e. **1,2,3**.

**Interquartile range formula**

**IQR = Q3 - Q1**

Where **Q3 **and **Q1 **are the third and first quartiles respectively.

## How to find Quartiles?

**Example**

For the following set of data, find the **1st **and **3rd **quartiles. Also, find **IQR**.

3, 1, 6, 9, 12, 15, 18

**Solution:**

**Step 1:** Arrange the values in ascending order.

`1, 3, 6, 9, 12, 15, 18`

**Step 2:** Put the values in the quartile formula for the first quartile.

`Q1 = 1(n+1)`

^{th}/4 term

Q1 = 1(7+1)^{th}/4 term

Q1 = (8)^{th}/4 term

Q1 = 2nd term

**2nd** term is **3**. So,

`Q1 = 3`

**Step 3:** Put the values in the quartile formula for the third quartile.

`Q3 = 3(n+1)`

^{th}/4 term

Q3 = 3(7+1)^{th}/4 term

Q3 = 24^{th}/4 term

Q3 = 6th term

**6th** term is **15**. So,

`Q3 = 15`

**Step 4:** Put these values in the interquartile formula or use the **IQR **calculator above.

`IQR = Q3 - Q1`

IQR = 15 - 3

`IQR = `

**12**