Quartile Deviation

Quartile Deviation

Quartile Deviation

For the quartile deviation, let us have an idea about the quartiles. We know that the median divides the given observations, arranged in ascending or descending order into two equal parts. Similarly, the quartiles divides the given observations into four equal parts after arranging them in ascending or descending order. So there are three quartiles denoted by Q1, Q2 and Q3 known as the first, the second and the third quartiles respectively.

If N be the number of observations of the given data. So after arranging them in the ascending or descending order the quartiles are given by:        
Quartiles for discrete data

In case of continuous frequency distribution, the quartiles are calculated by the following formula:      
Quartiles for continuous data

Where, L= lower limit of the quartile class
           f = frequency of the quartile class
          cf = cumulative frequency of preceding class
           i = height of class-interval

The difference between the third and the first quartile is called inter quartile range.

   i.e.       Inter Quartile Range = Q3 – Q1

The average of deviation of the first quartile and the third quartile taken from median (M) is called the quartile deviation or semi-interquartile range.

quartile deviation

As the units of quartile deviations is same as that of the given observation, the two distribution with different units can not be compared by quartile deviation. To faciliate the comparision of the quartiles of two or more than two series, a relative measure, the coefficient of quartile deviation is used where,
           
coefficient of quartile deviation


Workout Examples

Example 1: Calculate the quartile deviation and its coefficient of the following data:

                   24, 32, 46, 48, 39, 42, 28, 25, 26, 24, 38

Solution: Here,
                        Arranging the data in ascending order,
                        24, 24, 25, 26, 28, 32, 38, 39, 42, 46, 48
                        No. of data (N) = 11
            
Example 1: Solution

            Hence, quartile deviation = 8.5 and its coefficient = 0.25.


Example 2: Calculate the quartile deviation and its coefficient from the following data:       
      
Ages
12
13
14
15
16
17
18
No. of Students
12
21
15
20
17
10
5

Solution: Here,

Ages (in years)
No. of Students (f)
Cumulative frequency (cf)
12
13
14
15
16
17
18
12
21
15
20
17
10
5
12
33
48
68
85
95
100

N = 100


            Here, N = 100            
Example 2: Solution

            Hence, quartile deviation = 1.5 and its coefficient = 0.103.


Example 3: Calculate the quartile deviation and its coefficient from the following data:       
      
Marks
0-20
20-40
40-60
60-80
80-100
No. of Students
12
20
25
18
5

Solution: Here,

Marks
No. of Students (f)
Cumulative frequency (cf)
0-20
20-40
40-60
60-80
80-100
12
20
25
18
5
12
32
57
75
80

N = 80


            Here, N = 80                       
Example 3: Solution

            Hence, quartile deviation = 17.67 and its coefficient = 0.39.


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