Quartile Calculator

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 (1^st quartile): The lower/ 1^st quartile is the median of the 1^st 25% of the data set
2. Q₂ (2^nd quartile): The 2^nd quartile is also known as the median of a sample space.
3. Q₃ (3^rd quartile): The 3^rd 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 = 3^rd term

The 3^rd 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 = 9^th term

9^th term is 76 so,

Q₃ = 76

For IQR:

IQR = Q3 – Q1

IQR = 76 – 5

IQR = 71

References

• What are quartiles? | Wikipedia.
• Formulas of quartiles. (n.d.).