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Quartile Calculator



How to Use Quartile Calculator?

  • Enter the comma-separated values.
  • Click on the “calculate” button.
  • Hit the reset button to enter new values.





Quartiles Calculator


Quartile calculator finds the order, interquartile range, first quartile, second quartile, and third quartile respectively of the entered data set.


What are quartiles?


The quartiles are the percentiles that divide the whole data into 4 equal parts, there are three types of quartiles.

  1. Q1 (1st quartile): The lower/ 1st quartile is the median of the 1st 25% of the data set
  2. Q2 (2nd quartile): The 2nd quartile is also known as the median of a sample space.
  3. Q3 (3rd quartile): The 3rd quartile is the upper quartile of a data set that occupies the upper 25% of it.
  4. IQR (interquartile range): The IQR is the difference between Q3 and Q1.

Formulas of quartiles:


There are several formulas to calculate the quartiles of a data set, these are as follows:

Let “n” be the number of terms of a data set, then the quartiles can be given as

Q1 = {1(n +1)th / 4} term

Q2 = {2(n +1)th / 4} term

Q3 = {3(n +1)th / 4} term

IQR = Q3 – Q1


How to calculate quartiles of a data set?


In the below examples, the method of finding quartiles is explained briefly.

Example 1:

Find Q1, Q2, Q3, and IQR of the set 9, 4, 5, 54, 76, 23, 95, 20, 74, 82, 9, 1.

Solution:

The data set is 9, 4, 5, 54, 76, 23, 95, 20, 74, 82, 1

Step 1: Arrange the data set in ascending order.

1, 4, 5, 9, 20, 23, 54, 74, 76, 82, 95

Step 2: Calculate the total number of terms “n”

Total terms = n = 11

Now calculate Q1, Q2, Q3, and IQR respectively.


For Q1:


The formula for Q1 is:

Q1 = {1(n +1) th / 4} term

Q1 = {1 (11+1) th / 4} term

Q1 = {(12) th / 4} term

Q1 = 3rd term

The 3rd term of the sequenced set is 5 so,

Q1 = 5


For Q2:


As Q2 is the median of the data set and the median is the central term of a sequenced set.

The set is 1, 4, 5, 9, 20, 23, 54, 74, 76, 82, 95

The central value is “23


For Q3:


Q3 = {3(n +1) th / 4} term

Q3 = {3(11+1) th / 4} term

Q3 = {3(12) th / 4} term

Q3 = {(36) th / 4} term

Q3 = 9th term

9th term is 76 so,

Q3 = 76


For IQR:


IQR = Q3 – Q1

IQR = 76 – 5

IQR = 71


References