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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.

Graphically, the quartiles can be displayed as: ## 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