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Quartile Calculator

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)
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If you don’t know the above terms, we will elaborate on each one of them for you in the below sections. In this Content, we will explain the 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.

How does quartiles calculator work?

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.

What is quartile?

Wikipedia states that,

“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:

1st quartile

The first quartile represents the 25th 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.

2nd quartile

The second quartile represents the 50th 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.

3rd quartile

The third quartile represents the 75th 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.

Interquartile range

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.

Interquartile

Formula to calculate quartiles

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

First quartile formula

The first quartile Q1 formula can be stated as:

Q1= ¼ (n + 1) th term

Second quartile formula

The second quartile Q2 formula can be stated as:

Q2 = ½ (n + 1) th term

Third quartile formula

The third quartile Q3 formula can be stated as:

Q3= ¾ (n + 1) th term

Interquartile range formula

The interquartile range formula can be stated as:

IQR = Q3 – Q1

How to calculate quartiles?

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

Example – Data set having an odd number of values

Calculate the 1st, 2nd, and 3rd 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 median Q2 of the data set. As you can see, the data set contains an odd number of values. Start removing the values one by one from both sides of the data set. The remaining value will be the median or second quartile Q2. In this case,

Second quartile Q2 = 6

Quartile

Step 3: Calculate the median of the lower half of the data set. It is the value of the first quartile Q1.

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 Q3.

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 by subtracting the first quartile Q1 from the third quartile Q3.

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

Example – Data set having even number of values

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 median Q2 of the data set. In this case, the data set contains an even number of values in it. To calculate the median of an even number of values, remove the values from both sides one by one. You will get two values in the middle. Add both values and divide them by 2 to get the median.

Quartie Calculator

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 Q1.

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 Q3.

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

Third quartile Q3 = 11

Step 5: Calculate the interquartile range by subtracting the first quartile Q1 from the third quartile Q3.

IQR = Q3 – Q1

IQR = 11 – 3 = 8

Here is the summary of these calculations:

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

FAQs

How do you calculate quartiles?

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 = 2nd term = 4

Q2 = ½ (n + 1) th term = ½ (7 + 1) th term = 4th term = 7

Q3= ¾ (n + 1) th term = ¾ (7 + 1) th term = 6th term = 10

IQR = Q3 – Q1 = 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

What is the formula for lower quartile?

The formula for lower quartile is:

Q1= ¼ (n + 1) th term

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

How do you calculate the interquartile range?

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

IQR = Q3 – Q1

What are the 4 quartiles?

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.