Coefficient of Quartile Deviation

If you’re looking for an in-depth guide on the coefficient of quartile deviation, you’ve come to the right place! In this article, we’ll discuss what the coefficient of quartile deviation is, how to calculate it, and how to use it in real-world scenarios. We’ll also provide a few examples so that you can see how this statistic can be used effectively. So, without further ado, let’s get started!

What are Quartiles?

Quartiles are the values that divide a group of observations into four equal parts. The first quartile, denoted by Q_₁ is defined as the 25th percentile, the second quartile (Q_₂) is defined as the 50th percentile (median), and the third quartile (Q_₃) is defined as the 75th percentile. Quartiles can be computed for ungrouped data and for grouped data.

What is the coefficient of quartile deviation?

The coefficient of quartile deviation is a measure of dispersion, which is used to describe the spread or distribution of data. It is calculated as follows:

Coefficient of quartile deviation = (Q75 – Q25) / (Q75 + Q25)

This statistic is most commonly used with grouped data, which is data that has been organized into intervals or categories.

How to calculate the coefficient of quartile deviation?

To calculate the coefficient of quartile deviation, you need to follow these steps:

– Step One: Calculate the first and third quartiles by using the formula (n+l)/(n+h) where n=number of items in the list, l=lower quartile, h=higher quartile.

– Step Two: Subtract the lower quartile from the higher quartile.

– Step Three: Square this result.

– Step Four: Take the square root of this result.

– Step Five: Multiply your answer by 100 to get a percentage value for the coefficient of quartile deviation.

The coefficient of quartile deviation is a measure of the spread or variability of a set of data. It is calculated by taking the difference between the upper and lower quartiles, squaring it, and then taking the square root. It is expressed as a percentage, making it easy to compare data sets. It can be used to identify unusual values in a set of data and to measure the degree of variation within a data set. The coefficient of quartile deviation is a valuable tool for data analysis and can help to identify trends in data. It is also a good way to compare two or more data sets.

Coefficient of quartile deviation formula

The coefficient of quartile deviation formula is given as,

Coefficient of Quartile Deviation (Q) = Q₃-Q₁/Mean × (Std.Dev.)

Where,

Q₁ is the lower quartile,

Q₃ is the upper quartile,

Mean is the arithmetic mean of all observations, and

Std. Dev. is the standard deviation of all observations.

The coefficient of quartile deviation is the ratio between the difference between the first and third quartile to their mean. It shows how much the data is spread in the lower and upper half of the set.

Coefficient of Quartile Deviation for Grouped Data

The coefficient of quartile deviation for grouped data is the same as that of ungrouped data. It is calculated by using the same formula as the Coefficient of quartile deviation for ungrouped data.

The formula of Coefficient of Quartile Deviation for Grouped Data:

Before finding the Coefficient of Quartile Deviation for Grouped Data, 

we need to know how to find ₁th using this formula,

Q₁ = l₁+((r₁N/4 – CF) / f ) x h; 

r₁ = 1,2,3

where

l =  the lower limit of the  quartile class

N =total number of observations

 f = frequency of the  quartile class

CF = cumulative frequency of the class previous to  quartile class

h =  the class width

Now, the formula of Coefficient of Quartile Deviation for Grouped Data is, 

CQD =(Q₃ – Q₁)/(Q₃ + Q₁)

Where, 

Q₁ is quartile first 

Q₃ is quartile three

Merits of Coefficient of Quartile Deviation

Merits of Coefficient of Quartile Deviation are as follows:

It is less sensitive to fluctuations. It can be calculated for a grouped series also, but it does not have many uses in the field of business or commerce unless supplemented by some other measure.

Limitations of Coefficient of Quartile Deviation

Limitations of Coefficient of Quartile Deviationare as follows:

It has no direct interpretation and its value cannot be reduced to a single value. It is not suitable for the qualitative data as it does not indicate any tendency of clustering around the mean or median.

Conclusion 

The coefficient of quartile deviation is a statistic that can be used to measure the spread of data. It is especially useful when comparing different sets of data. In this guide, we’ve explained what the coefficient of quartile deviation is and how it can be used. We’ve also provided examples so you can see how it works in practice.