Quartile Deviation Formula
Statistics is the branch of mathematics that deals with the compilation and calculations of data. It is the single biggest field of research in Mathematics and Computer science today with Automation being done at a rapid pace and billions of bytes of data available online. One of the more important topics of statistics is known as Quartile deviation. The concept of quartile deviation finds relevance when we have to assess the spread of a distribution. The important thing we have to usually find out using statistical tools is the distribution measures and their spread from its central tendency (known as ‘the mean’). So, quartile deviation provides helpful insight into the segmentation and within which the central 50% of your sample data lies.
Importance of Quartile Deviation
Statistics is about understanding the art and science of the collection of data, the frequency, and the distribution of the trends. The accepted definition of Quartile deviation is the difference between the first quartile and the third quartile in the frequency distribution table. This difference is known as the interquartile range. The interquartile range is important as this is the spread of the data that is most important and from this point, numerous regressions and deviations can be calculated which are very helpful to assess the characteristics of the data. When the difference is divided by two, it is known as quartile deviation or semi-inter-quartile range.
Here is an example to help you understand better.
If a set of 13 numbers is given to you, then the median would be the seventh number. The six numbers above are the lowest in the data. The six numbers after the median are the highest number in the given data. So, it is natural to say that the median is not affected by extreme values. This is where the quartile comes in. These Quartiles help to measure the spread of values above and below the mean by dividing the data into four groups.
That is where the quartile steps in. The quartile measures the spread of values above and below the mean by dividing the distribution into four groups. So you have first, second, and third quartiles written as Q1, Q2, and Q3 respectively. Q2 is the median. To find quartiles in a grouped data, we have to arrange the data. The information is always arranged in ascending order.
Quartile Formula
Let us assume that-
Q3 is the upper quartile in the median of the upper half of the data sample.
Q1is the lower quartile and median of the lower half of the data.
Median is Q2.
Number of items in data is n, the quartiles are given by
Q1= (n+1)/4(n+1)/4th item
Q2=(n+1)/2(n+1)/2th item
Q3=3(n+1)/43(n+1)/4th item
Hence, the formula for quartile can be written as
Qr= \[1 + \frac {r(n/4)-c(2-1)} {f}\]
Where, Qr is the rth quartile, l1 is the lower limit, l2 is the upper limit, f is the frequency, and c is the cumulative frequency of the class preceding the quartile class.
About Quartile Deviation
We can define Quartile deviation as half of the distance between the third and the first quartile. It is also known as the Semi Interquartile range. When one takes half of the difference or variance between the 3rd and the 1st quartiles of a simple distribution or frequency distribution it is quartile deviation.
The quartile deviation formula is
Q.D. = Q3-Q1/ 2
Example –
Quartiles are values that divide a list of numbers into quarters. Put the numbers in ascending order, then cut the list in four equal parts. The quartiles are the cuts.
For example- 5, 7, 4, 4, 6, 2, and 8.
Arrange them in order – 2, 4, 4, 5, 6, 7, and 8.
Cut the list into quarters.
Quartile 1 (Q1) = 4 or lower quartile
Quartile 2 (Q2) = which is also the Median = 5
Quartile 3 (Q3) = 7 or lower quartile
FAQs on Quartile Deviation
1. Why do we calculate the quartile deviation?
The quartile deviation helps to examine the spread of a distribution about a measure of its central tendency, usually the mean or the average. Hence, it is in use to give you an idea about the range within which the central 50% of your sample data lies. Quartiles are in use for reporting on a set of data and for making box and whisker plots. Quartiles are of particular use when the data does not have a symmetrical distribution. HR teams use it to determine what salary range to provide to an employee / new joinee based on his experience and qualifications.
2. What is the role of quartiles in statistics?
Quartiles divide the given data into four groups (after the data is sorted). Each group contains an equal number of values. Quartiles are divided by the 25th, 50th, and the 75th percentile, also called as first, second, and the third quartile. Quartile splits the collected data into quarters so that 25 percent of the estimations are less than the lower quartiles, 50 percent of the estimations are less than the mean, and 75 percent of the estimations are less than the upper quartile. In order to understand it better, let us arrange it in the following way:
First quartile= 25% from smallest to largest numbers
Second quartile = between 25.1% and 50 % i.e. the median
Third quartile = 51 % to 75% i.e. above the median
Fourth quartile = 25% of the largest numbers
3. What are the mean and median?
The mean and median are terms used in statistics that are used to signify the central tendency of a data set. Mean and median are both used to signify the central or middle character of a dataset however both are very different when it comes to the formulation. Mean is generally the average value of the dataset while the median is the middle number in sorted order, ascending or descending.
4. What is the practical significance of quartile deviation?
Once you have found out the quartile deviation, you can then proceed to find out the interquartile range which is a very important tool in statistics. For finding out the quartile deviation you have to establish the mean of the data set. Once you have found the quartile deviation, you then have to proceed to find out the interquartile range from which you can establish what is the frequency and distribution of the data.
5. What is the role of quartiles in statistics?
Quartiles as the name suggest dividing the given data into a set of four groups after the data is sorted. Quartiles are divided by the 25th, 50th, 75th percentile which is also known as first quartile, second quartile, and third quartile respectively. This separates the data into quartiles which means the data can be categorized as lying above or below the median. For ex- The Fourth quartile will consist of 25% of the largest numbers.
6. Which courses require the use of high-level statistics like quartile deviation?
Statistics is something which has been used in almost every field nowadays in some form or the other. However, there are some courses that require very focused use of statistics like Computer Engineering, MSc in Mathematics, Economics, etc. It is always a good idea to have a good hold of the subject as even in the job sector in fields like Business Analyst and Data Interpretation, Statistics are very highly relied upon.
7. I am facing troubles while solving the exercises on quartile deviation, what shall I do?
It is natural for students to face issues when they are trying advanced mathematics topics like quartile deviation for the first time. The important thing is to take your own time and learn the basics of the subject. Ask whatever doubts you may be having with your teachers and discuss these questions with your friends. Vedantu provides high-quality subject material for students which are very easily accessible to them so try to make the most out of them