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# Quartile Calculator

Quartile Calculator is an online tool that helps to calculate the first, second, and third quartiles as well as the interquartile range for the given data set. Quartile divides the data into four parts whereas median divides the data into two parts.

## What is Quartile Calculator?

Quartile calculator helps to arrange the given data in ascending order and determines the three quartiles as well as the interquartile range for the given set of observations. To use the **quartile calculator**, enter the values in the input box within brackets, separated by commas.

### Quartile Calculator

**NOTE:** Please enter the values inside the bracket separated by commas.

## How to Use the Quartile Calculator?

Please follow the steps given to find the quartiles and the interquartile range for the given data set using the online quartile calculator:

**Step 1:**Go to Cuemath's online quartile calculator**Step 2:**Enter the data set separated by commas within brackets in the given input box.**Step 3:**Click on the**"Calculate"**button to find the quartiles and the interquartile range for the given data set.**Step 4:**Click on the**"Reset"**button to clear the field and enter new values.

## How Does Quartile Calculator Work?

Any given data set will have three quartiles. These are as follows:

**First Quartile (Q1):**This is also known as the lower quartile. The first quartile lies between the first term and the median of the given set of observations.**Second Quartile (Q2):**This is the median of the data set.**Third Quartile (Q3):**This is the middle value of the median and the last term. Further, Q3 is known as the upper quartile

Interquartile Range (IQR) can be defined as the distance between the highest quartile and the lowest quartile. The formula is given as follows:

IQR = Q3 - Q1.

Steps to find the Quartile of the data set:

- Arrange the data set in increasing order.
- Determine the median of the data set. This will be Q2. If the data set is odd the median is the middle point of the data. If the data set is even the median is the average of the two middle points.
- If the number of observations is odd then we exclude the median (Q2) while splitting the data set equally into two. If the data set is even we split the complete set equally into two groups.
- To determine Q1, take the lower half of the data and find its median.
- To determine Q3, take the upper half of the data and find its median.

## Solved Examples on Quartile Calculator

**Example 1:**

Find the quartiles of {2, 1, 5, 1, 4, 3, 8} and the IQR. Verify it using the online quartile calculator.

**Solution: **

Arranging the data is ascending order we have {1, 1, 2, 3, 4, 5, 8}

n = 7.

As n is odd

Median Q2 = 3.

Lower half of the data set {1, 1, 2}

Middle value Q1 = 1.

Upper half of data set {4, 5, 8}

Middle value Q3 = 5

IQR = Q3 - Q1

= 5 - 1

= 4.

Q1 = 1, Q2 = 3, Q3 = 5, IQR = 4

**Example 2:**

Find the quartiles of {2, 7, 3, 2, 5, 1} and the IQR. Verify it using the online quartile calculator.

**Solution:**

Arranging the data is ascending order we have {1, 2, 2, 3, 5, 7}

n = 6.

As n is even,

Find the median of the data set.

Q2 = (1/2) [(n/2)th observation and ((n/2) + 1)th observation]

= (1/2)[3^{rd} observation + 4^{th} observation]

= (1/2) [2 + 3]

= 2.5

Lower half of the data set {1, 2, 2}

Middle value Q1 = 2

Upper half of data set {3, 5, 7}

Middle Value Q3 = 5.

IQR = Q3 - Q1 = 5 - 2 = 3

Q1 = 2, Q2 = 2.5, Q3 = 5, IQR = 5

Similarly, you can try the quartile calculator to find the quartile for the given data sets

- {6, 1, 5, 9, 3,15, 8}
- {8, 12, 1, 9, 15, 16, 1, 8}

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