Quartile Calculator


What is Quartile Calculator?

'Cuemath's Quartile Calculator' is an online tool that helps to calculate the quartile for a given data set. Cuemath's online quartile calculator helps you to calculate the quartile for a given data set within a few seconds.

NOTE: Please enter the values inside the bracket and seperated by comma.

How to Use the Quartile Calculator?

Please follow the below steps to find the quartile for a given data set:

  • Step 1: Enter the data set separated by a comma in the given input box.
  • Step 2: Click on the "Calculate" button to find the quartile for a given data set.
  • Step 3: Click on the "Reset" button to find the quartile for a given data set for different data set.

How to Find the Quartile? 

Quartile means a quantile that divides a ranked data into four equal parts. The Quartile which divides a given data set into four equal parts is known as the First quartile- Q1, second quartile- Q2, and Third quartile- Q3 respectively. The first quartile is also known as the lower quartile. 

  • Q1 is the mid-value of the first half 
  • Q2 is the Median
  • Q3 is the mid-value of the second half or last half.

The first quartile (or lower quartile) is the median or mid-value of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

The second quartile is the median of the given data set.

The third quartile is the median or mid-value of the second half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

The intermediate quartile is defined as the difference between the third quartile(Q3) and the first quartile(Q1)

Intermediate quartile(IQR) = Q3 - Q1

Note: 1) If the given data set has even numbers, Find the median from the bottom half and upper half

          2) If the given data set has odd numbers, Find the median or average from the bottom half and upper half

Solved Example 1:

Find the quartile from the given data set { 8, 6, 9, 2, 4, 5 }

Solution:

Number of terms = 6

Arrange this data set in increasing order i.e., {2, 4, 5, 6, 8, 9}

So, the bottom half is { 2, 4, 5 } and the upper half is {6, 8, 9}

The median of the bottom half(Q1) for { 2, 4, 5 } is 4.

The median of a given data set(Q2) for {2, 4, 5, 6, 8, 9} is 5.5

The median of the upper half(Q3) for {6, 8, 9} is 8

Intermediate quartile(IQR) = Q3 - Q1 

= 8 - 4

= 4

Solved Example 2:

Find the quartile from the given data set { 8, 6, 9, 2, 5 }

Solution:

Number of terms = 5

Arrange this data set in increasing order i.e., {2, 5, 6, 8, 9}

So, the bottom half is {2,5} and the upper half is {8, 9}

The median of the bottom half(Q1) for {2, 5} is 3.5.

The median of a given data set(Q2) for {2, 5, 6, 8, 9} is 6.

The median of the upper half(Q3) for {8, 9} is 8.5.

Intermediate quartile(IQR) = Q3 - Q1 

= 8.5 - 3.5

= 5

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

1) {6, 1, 5, 9, 3,15, 8}     2) {8, 12, 1, 9, 15, 16}

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