Quartile Calculator

Quartile calculator is used to find the first, second, third, and inter quartiles of the given numbers. This q1 q2 q3 calculator also calculates the ascending and descending orders of the given list of numbers. 

What is a quartile?

A quartile is a type of quantile that has three points separated into four equivalent classes, each of which accounts for a fourth of the dispersed population.
There is a total of three quartiles in a data set:

1. The first quartile (Q₁)

The first quartile also referred to as the lower quartile, is equal to the 25th percentile of the data. The Q₁ separates the lowest 25% of data from the highest 75%.

2. The second quartile (Q₂)

The second quartile, also known as the middle quartile or median of a data set is equal to the 50th percentile of the data. It cuts data in half.

3. The third quartile (Q₃)

The third quartile, also known as the upper quartile (QU), represents the 75th percentile of the data. It separates the lowest 75% of data from the highest 25%.

Quartile formula

The formula for various quartiles can be written as follow:

The Quartile Formula for Q₁

The quartile formula for Q1 or first quartile formula can be expressed as:

Q₁= \(\dfrac{1(n+1)^{th}}{4}\) term

The Quartile Formula for Q₃

The quartile formula for Q3 or third quartile formula can be expressed as:

Q₃= \(\dfrac{3(n+1)^{th}}{4}\) term 

The Quartile Formula for Q₂

The quartile formula for Q3 or third quartile or median formula can be expressed as:

Q₂ =  \(\dfrac{(n+1)^{th}}{2}\) term

Interquartile Range (IQR)

The quartile formula for interquartile range IQR can be expressed as:

IQR = Q₃ – Q₁

How to calculate quartiles?

Example

Find all the quartiles for the group below:

\(2, 4, 3, 7, 8, 1, 10\)

Solution

Step 1: Arrange the data in ascending order.

\(1, 2, 3, 4, 7, 8, 10\)

Step 2: Find the first Quartile (Q₁):

Q₁= \(\dfrac{1(n+1)^{th}}{4}\) term

Q₁= \(\dfrac{1(7+1)^{th}}{4}\) term

Q₁= \(\dfrac{8}{4}^{th}\) term

Q₁= \(2^{nd}\) term which is 2. 

Step 3: Find the second Quartile (Q₂):

Q₂= \(\dfrac{2(n+1)^{th}}{4}\) term

Q₂= \(\dfrac{2(7+1)^{th}}{4}\) term

Q₂= \(\dfrac{16}{4}^{th}\) term

Q₂= \(4^{th}\) term which is 4. 

Step 4: Find the third Quartile (Q₃):

Q₃= \(\dfrac{3(n+1)^{th}}{4}\) term

Q₃= \(\dfrac{3(7+1)^{th}}{4}\) term

Q₃= \(\dfrac{24}{4}^{th}\) term

Q₃= \(6^{th}\) term which is 8.