Generalized Formula for Quartile
The generalized formula for the quartile is,
[Tex]\bold{\text{Quartile}_r = l_1 + ( i\cdot \frac{n}{4} – c_f) \cdot \frac{(l_2-l_1)}{f}} [/Tex]
Where,
- Quartiler indicates rth quartile.
- l1, l2 are lower and upper limit value that contains ith quartile,
- f is the frequency count.
- cf is the cumulative frequency of class preceding the quartile class.
Using this generalized formula, the first and third quartiles can be calculated as:
- [Tex]\bold{\text{Q}_1 = l_1 + ( \frac{n}{4} – c_f) \cdot \frac{(l_2-l_1)}{f}} [/Tex]
- [Tex]\bold{\text{Q}_3 = l_1 + ( \frac{3n}{4} – c_f) \cdot \frac{(l_2-l_1)}{f}} [/Tex]
Interquartile Range
Interquartile Range is the distance between the first quartile and the third quartile. It is also known as a mid-spread. It helps us to calculate variation for the data which is divided into quartiles. The formula for calculating the Interquartile range is given by,
Interquartile Range (IQR) = Q3 – Q1
Where,
- Q3 is third/upper quartile, and
- Q1 is first/lower quartile.
Quartile Deviation
Quartile Deviation is defined as half of the distance between the first quartile and the third quartile. It is also known as Semi Interquartile Range. The formula for quartile deviation is given by,
Quartile Deviation = (Q3 – Q2)/2
Quartile Formula
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.
Table of Content
- Quartiles Definition
- What is the Quartile Formula?
- Quartiles in Statistics
- Generalized Formula for Quartile
- Quartile vs Percentile
- Solved Problems on Quartile Formula
- Quartile Formula Practice Probems