Quartiles

Quartile is a branch of statistics that is a type of quantile. This divides any given data set into four parts (or quarters) of the same size as possible. The second quartile is the median of the data set. The first quartile is the point exactly between the smallest number and the median of the set. Quartiles can be identified in a given data set using Quartile Deviation. The Quartile deviation formula is Q.D(Quartile Deviation) and is equal to (Q3 – Q1)/2. In simple words, it is a method to measure the deviation. It calculates the deviation of the given data from an average value. The quartile deviation helps us to understand the distribution of data by spreading data. Let’s understand this in brief. 

Quartile Deviation 

A quartile deviation is a tool to measure the changes or deviation by spreading or dividing the given data into four equal parts and after that, comparing the final result with the given set of data. Quartile deviation is used for whisker and box plot. The quartiles divide the total given data into free quarters. These three quarters are as follows. 

1. The first quartile Q1 is the median of the lower class of the data. This shows that around 25% of the given data comes under the first quartile and the rest 75℅ comes above the first quarter. 
2. The second quartile is known as Q2 is the median which divides the entire data into two parts of 50℅ each. This means 50℅of the data fall below and comes above the Q2. 
3. The third quartile is Q3, the median comes under the upper range of the data which shows that 75% of the data comes below this quartile and the rest 25℅ is above. 

Quartile Deviation Formula

As discussed above, quartile deviation is a median that splits the data into four equal parts or in three quarters which measure the data below and above the mean. The Quartile Deviation Formula is-

QD- (Q3 – Q1)/2 

Or

Quartile Deviation- (Third Quartile –First Quartile) /2

Quartile Deviation Calculation 

Quartile Deviation can be easily calculated for grouped and ungrouped data. Quartile Deviation is a tool which measures the level of dispersion that is not being affected by the extreme values. The quartile deviation is calculated in two types of methods which are mainly dependent on the given data in the question. As mentioned above, it is calculated for grouped and ungrouped data. The steps for calculating the Quartile Deviation are:

1. Arrange the data given in the question in ascending order. 
2. Then find out the value of the first quartile. For grouped data, use:

Q1= (n+1)/4

For ungrouped data, use

Q1= l1 +((N/4)- c)x (l2-l1)/f

Where 

n is the particular quartile. 

N is the sum of total frequency. 

f is the frequency of the particular class. 

c is the preceding class’s cumulative frequency. 

l1 is the lower class. 

l2 is the upper class. 

For the Q3, which is the third quartile, the formula for ungrouped data is:

Q3= 3(n+1)/4

For grouped data, use

Q3=l1 + (3(N/4) –c) (l2-l1)/ f

Then after speculating both the quartiles, calculate the quartile deviation using:

QD= (Q3 – Q1)/2. 

The need for Quartile Deviation 

The most important benefit of quartile deviation is that it divides the data set into four equal parts to analyze the sets of the data set. Here’s an example.

Suppose an employer has given its workers from Rs 10 to Rs 100. And to the top performer worker with 25℅, while for underperformed workers by 25℅ and the average workers, as 50℅. Now if the total workers are 4 who all have earned 55, 25, 75, and 95. Then it’s easy to calculate that the worker with the earnings of 95 performed the best while another with 25 performed the least and the middle other two workers performed average. This is possible with the help of quartile deviation. 

Coefficient of Quartile Deviation 

The relative measure of dispersion based on quartiles is known as the coefficient of quartile deviation. The coefficient of quartile deviation which is also known as the quartile coefficient of dispersion lets you make a comparison of dispersion between two or more sets of variables. The formula for the Coefficient of quartile deviation is

Coefficient of quartile deviation=(Q3 – Q1) X 100/Q3 + Q1

The coefficient of quartile deviation includes two numbers of the same dimensions and thus it’s unitless. This is the reason why it is best for comparing two or more sets of data even if they didn’t involve the quantity of equal dimensions.

Conclusion 

Quartile Deviation is a tool through which we measure the deviation or suspension in the middle of the given data which shows the spread of data. Quartile deviation values are half of the difference between Q3 and Q1. So here we discussed Quartile Deviation, its importance, Its formula, and Coefficient.