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Quartile calculator** **is an online statistical calculator that finds the value of quartile in a given range. It is very easy to use tool to quickly get the quartile range sorted out for your statistics problems. This IQR calculator calculates the:

- Interquartile Range (IQR)
- 1st Quartile (Q1)
- 2nd Quartile (Q2)
- 3rd Quartile (Q3)

If you don’t know the above terms, we will elaborate on each one of them for you in the below sections. In this post, we will explain quartiles definition, **how do you find q1 and q3, how to find the interquartile range, **how can you use first quartile calculator** **to find quartiles, and some examples to make this topic clear to you.

Quartile Calculator

Table of Contents:

Some of the quartile calculations can be daunting because it involves several calculations along with calculations of the median for each quartile. That is why, we come up with this idea to automate the quartile range, q1, and q3 calculations for the ease of students and researchers.

The** **interquartile range calculator** **simplifies the whole process. You don’t have to struggle to find averages and medians to get your quartile range, etc. Just feed the input values to this calculator to see how it functions.

To use this calculator, follow the below steps:

- Enter the data set in the given input box.
- Separate each value using a comma.
- Hit the
**Calculate**button to get the quartile values. - Use the
**Reset**button to enter new values.

You will instantly get the interquartile range (IQR), 1st Quartile (Q1), 2nd Quartile (Q2), and 3rd Quartile (Q3) as soon as you click that button. Use this calculator for learning purposes.

This tool is also referred to as the mean median and mode calculator** **because it calculates the quartile values by calculating the median of the lower range and upper range of the values.

“A quartile is a type of quantile which divides the number of data points into four more or less equal parts, or quarters.”

A quartile represents the specific part of a data set. It could be the first quarter, second quarter, or the third quarter of a data set. A set of data contains:

The first quartile represents the 25^{th} percentile of the data set. It divides the data into a lower 25 percent and also known as **lower quartile.** It is denoted by **Q1.**

The second quartile represents the 50^{th} percentile of the data set. It divides the data into half or 50 percent and also known as the **median.** It is denoted by **Q2.**

The third quartile represents the 75^{th} percentile of the data set. It divides the data into 75 percent from the remaining data set and also known as the **upper quartile.** It is denoted by **Q3.**

It is the difference between the upper quartile **Q3** and the lower quartile **Q1**. The interquartile range is denoted by **IQR. **It is also known as H-spread in statistics.

The quartile formulas are different for each type of quartile. The following formulas can be used to calculate interquartile range, lower, and upper quartile.

The first quartile Q1 formula can be stated as:

**Q1= ¼ (n + 1) ^{ th} term**

The second quartile Q2 formula can be stated as:

**Q2 = ½ (n + 1) ^{th} term**

The third quartile Q3 formula can be stated as:

**Q3= ¾ (n + 1) ^{ th} term**

The interquartile range formula can be stated as:

**IQR = Q _{3} – Q_{1}**

Are you wondering** how to find quartile 1? **In this section, we are going we answer all your questions. Moreover, we will illustrate how to find quartiles** **in a set of data with examples. Get ready to manually calculate the q1, q2, q3, and IQR. You might find it a bit complicated at first, that’s why we have made these illustrative examples easy to understand.

To find quartiles in a data set, follow the below steps:

- The first step is to arrange the data. Arrange the data from the lowest number to the greatest (ascending form).
- After arranging the data, calculate the
**median****Q2**of the data set. The values on the left side of the median represent the lower half of the data set while values on the right side of the median represent the upper half of the data set. - Calculate the median of the lower half of the data set. It is the value of the first quartile
- Calculate the median of the upper half of the data set. It is the value of the third quartile
- Calculate the
**IQR**by subtracting the first quartile**Q1**from the third quartile

Calculate the 1^{st}, 2^{nd}, and 3^{rd} quartile along with the interquartile range in the following data set.

**Data set: 8, 3, 6, 2, 7, 12, 1, 5, 9**

__Solution__:

** Step 1:** Arrange the data in ascending form.

Arranged data set:** 1, 2, 3, 5, 6, 7, 8, 9, 12**

** Step 2: **Calculate the

**Second quartile** **Q2 = 6**

** Step 3:** Calculate the median of the lower half of the data set. It is the value of the first quartile

Lower half of the data set = **1, 2, 3, 5**

**First quartile Q1 = (2 + 3) / 2 = 5 / 2**

**Q1 = 2.5**

** Step 4:** Calculate the median of the upper half of the data set. It is the value of the third quartile

Upper half of the data set = **7, 8, 9, 12**

**Third quartile Q3 = (8 + 9) / 2 = 17 / 2**

**Q3 = 8.5**

** Step 5:** Calculate the

**IQR = Q3 – Q1**

**IQR = 8.5 – 2.5 = 6**

By summarizing the quartile calculations, we get:

**Q1 = 2.5, Q2 = 6, Q3 = 8.5, IQR = 6**

Find the first quartile, second quartile, third quartile, and IQR in the given data set.

**Data set: 5, 9, 3, 11, 14, 6, 1, 8**

__Solution__:

** Step 1:** Arrange the data in ascending form as in the previous example.

Arranged data set:** 1, 3, 5, 6, 8, 9, 11, 14**

** Step 2: **Find the

**Second quartile** **Q2 = (6 + 8) / 2 = 14 / 2 = 7**

** Step 3:** Calculate the median of the lower half of the data set. It is the value of the first quartile

The lower half of the data set = **1, 3, 5**

**First quartile Q1 = 3**

** Step 4:** Calculate the median of the upper half of the data set. It is the value of the third quartile

The upper half of the data set = **9, 11, 14**

**Third quartile Q3 = 11**

** Step 5:** Calculate the

**IQR = Q3 – Q1**

**IQR = 11 – 3 = 8**

Here is the summary of these calculations:

**Q1 = 3, Q2 = 7, Q3 = 11, IQR = 8**

Quartiles are used in statistics to divide a set of data into multiple parts. Suppose we have a list of numbers: 2, 4, 6, 7, 8, 10, 12. First, arrange the numbers in ascending order if they are not in order. Quartiles can be calculated by using the below formulas:

**Data set: 2, 4, 6, 7, 8, 10, 12**

**Q1= ¼ (n + 1) ^{ th} term = ¼ (7 + 1)^{ th} term = 2^{nd} term = 4**

**Q2 = ½ (n + 1) ^{th} term = ½ (7 + 1) ^{th} term = 4^{th} term = 7**

**Q3= ¾ (n + 1) ^{ th} term = ¾ (7 + 1)^{ th} term = 6^{th} term = 10**

**IQR = Q _{3} – Q_{1} = 10 – 4 = 6**

In these equations, **n **refers to the total number of values in a data set.

**2, 4, 6, 7, 8, 10, 12**

The formula for lower quartile is:

**Q1= ¼ (n + 1) ^{ th} term**

Where **n **represents the total number of values in a data set.

The interquartile range can be calculated by subtracting the first quartile from the third quartile.

**IQR = Q3 – Q1**

The 4 quartiles represent the data separated into various parts. The four quartiles are:

**The first quartile Q1: **Also referred to as lower quartile, is the lowest 25% of the data set.

**The second quartile Q2: **It is the median of the data set, also known as the middle quartile. It divides the data into two halves.

**The third quartile Q3: **Also referred to as the upper quartile. It represents the data between 51% and 75% of the data set.

**The fourth quartile Q4: **It represents the highest 25% of the data set.