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

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

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

Graphically, the quartiles can be displayed as:

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

*Q _{1} = {1(n +1)^{th} / 4} term *

*Q _{2} = {2(n +1)^{th} / 4} term *

*Q _{3} = {3(n +1)^{th} / 4} term *

*IQR = Q _{3} – Q_{1} *

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 **Q**_{1}, **Q**_{2}, **Q**_{3}, and IQR respectively.

**For Q _{1}: **

The formula for Q1 is:

*Q _{1} = {1(n +1)^{ th} / 4} term*

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

Q_{1} = {(12) ^{th} / 4} term

Q_{1} = 3^{rd} term

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

**Q _{1} = 5 **

**For Q _{2}:**

As Q_{2} 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 Q _{3}:**

*Q _{3} = {3(n +1)^{ th} / 4} term*

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

Q_{3} = {3(12) ^{th} / 4} term

Q_{3 }= {(36) ^{th} / 4} term

Q_{3} = 9^{th} term

9^{th} term is 76 so,

**Q _{3} = 76**

**For IQR:**

*IQR = Q3 – Q1*

IQR = 76 – 5

**IQR = 71**

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

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