Quartile Formula

What is a Quartile?

A quartile is a value in the dataset which divides the observations in four equal parts in terms of frequency. There are three quartiles in any data named as first, second and third quartile. 

What is the Formula for Finding the First Quartile?

The formula for first quartile (Q₁) is given as follows:

Q₁ = L + (N/4 – c_f) × (U – L)/F

Where,

• L is the Lower limit of the first quartile class,
• U is the Upper limit of the first quartile class,
• N is the Total number of observations, and 
• c_f is the Cumulative Frequency of the first quartile class (the class containing Q1)

What is the Formula for Finding the Second Quartile?

Second quartile (Q₂), also known as the median as it divides the data in two equal halves each containing equal number of observations as the other.

For n observation if n is odd, then median is

M = (n + 1)/2^th Observation

For n observation if n is even, then median is

M = [(n/2)^th Observation + ((n/2) + 1)^th Observation]/2

What is the Formula for Finding the Third Quartile?

The formula for finding the third quartile (Q₃) is:

Q₃ = L + (3N/4 – F) × (U – L)/F

Where,

• L is the Lower limit of the first quartile class,
• U is the Upper limit of the first quartile class,
• N is the Total number of observations, and 
• c_f is the Cumulative Frequency of the third quartile class (the class containing Q₃)

What is the Interquartile Range?

The interquartile range (IQR) is the difference between the third and first quartiles. It represents the middle 50% of the dataset and is given as follows:

IQR = Q₃ – Q₁

What is Quartile Deviation?

Quartile deviation is a measure of dispersion that is half the difference between the third and first quartiles of a dataset which mathematically can be represented as:

Quartile Deviation = (Q₃ – Q₂)/2

What is the Difference between Quartiles and Percentiles?

Quartiles divide data into four equal parts, while percentiles divide data into 100 equal parts.

Can Quartiles be Calculated for Non-Numerical Data?

No, quartiles are only applicable for numerical data.

Quartiles are the set of values that divide the data points into four identical values using three individual data points. Thus, a quartile is a very important topic in Statistics that helps us to study large amounts of data, they are used to divide the large data values into four equal quarters. These quartiles show the data that is near the middle points of the large data set.

In this article, we will learn about the quartiles as well as the formulas for the first quartile, second quartile, and third quartile and also provide a step-by-step guide to help you easily calculate quartiles. So, let’s start with the definition of quartile first.