Quartile Calculator

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Calculate all three quartiles (upper, middle, and lower) as well as the interquartile range (iqr) for the given data set using the quartile calculator.

Along with the quartile values, this calculator also provides a box graph, ascending descending arrangement of values, and median of the group.

How to use the Quartile Calculator?

To use this calculator, follow the steps given below:

  • Enter the data set as a quartile range in the given input box. Separate each value using a comma.
  • Press the Calculate button to see the results.

It will give you the calculated IQR, first quartile, second quartile, and third quartile.

MIN: 0
MAX: 0
Median: 0
First Quarter: 0
Second Quarter: 0
Third Quarter: 0
Inter Quartile: 0
Ascending: 0
Descending: 0
Graph:

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In this post, we will explain the quartile definition, how to find the first quartile and the lower quartiles, and the interquartile range.

What is a quartile?

A quartile is a type of quantile that has three points separated into four equivalent classes, each of which accounts for a fourth of the dispersed population.
There is a total of three quartiles in a data set:

1. The first quartile (Q1)

The first quartile also referred to as the lower quartile, is equal to the 25th percentile of the data. The Q1 separates the lowest 25% of data from the highest 75%.

2. The second quartile (Q2)

The second quartile, also known as the middle quartile or median of a data set is equal to the 50th percentile of the data. It cuts data in half.

3. The third quartile (Q3)

The third quartile, also known as the upper quartile (QU), represents the 75th percentile of the data. It separates the lowest 75% of data from the highest 25%.

Quartile formula

The formula for various quartiles can be written as follow:

The Quartile Formula for Q1

The quartile formula for Q1 or first quartile formula can be expressed as:

Q1= 1(n+1)th4\dfrac{1(n+1)^{th}}{4} term

The Quartile Formula for Q3

The quartile formula for Q3 or third quartile formula can be expressed as:

Q3= 3(n+1)th4\dfrac{3(n+1)^{th}}{4} term 

The Quartile Formula for Q2

The quartile formula for Q3 or third quartile or median formula can be expressed as:

Q2 =  (n+1)th2\dfrac{(n+1)^{th}}{2} term

Interquartile Range (IQR)

The quartile formula for interquartile range IQR can be expressed as:

IQR = Q3 – Q1

How to calculate quartiles?

Find all the quartiles for the group below:

2,4,3,7,8,1,102, 4, 3, 7, 8, 1, 10

Solution:

Arrange the data into ascending order.

1,2,3,4,7,8,101, 2, 3, 4, 7, 8, 10

First Quartile (Q1):

Q1= 1(n+1)th4\dfrac{1(n+1)^{th}}{4} term

Q1= 1(7+1)th4\dfrac{1(7+1)^{th}}{4} term

Q1= 84th\dfrac{8}{4}^{th} term

Q1= 2nd2^{nd} term which is 2

Second Quartile (Q2):

Q2= 2(n+1)th4\dfrac{2(n+1)^{th}}{4} term

Q2= 2(7+1)th4\dfrac{2(7+1)^{th}}{4} term

Q2= 164th\dfrac{16}{4}^{th} term

Q2= 4th4^{th} term which is 4

Third Quartile (Q3):

Q3= 3(n+1)th4\dfrac{3(n+1)^{th}}{4} term

Q3= 3(7+1)th4\dfrac{3(7+1)^{th}}{4} term

Q3= 244th\dfrac{24}{4}^{th} term

Q3= 6th6^{th} term which is 8

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