Quartiles

Quartiles

Quartiles

Quartiles are the values that divide the data arranged in ascending or descending order into  four equal parts. A distribution is divided into four equal parts by three quartiles.

-   The first or lower quatile (Q1) is the point below which 25% of the items lie and above which 75% of the items lie.
-   The second quartile (Q2) is the point below which 50 percent of the items lie and above which 50 % of the items lie. Of course, the second quartile is the median.
  The third (upper) quartile ( Q3 ) is the point below which 75 % of the items lie and above which 25 % of the items lie.

If N be the number of items in ascending or descending order of a distribution then in the case of individual and discrete data,
Quartiles for individual and discrete data

In case of the grouped data,        
Quartiles for grouped 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


Workout Examples

Example 1: Calculate the quartiles from the data: 4, 6, 5, 9, 8, 10, 3

Solution: Here,
                        Data in ascending order: 3, 4, 5, 6, 8, 9, 10
                        No. of data (N) = 7
            
Example 1: Solution


Example 2: Calculate the quartiles from the data: 5, 8, 10, 11, 12, 14, 16, 18, 20, 4

Solution: Here,
                        Data in ascending order: 4, 5, 8, 10, 11, 12, 14, 16, 18, 20
                        No. of data (N) = 10
           
Example 2: Solution


Example 3: Compute Q1 and Q3 from the following data.

x
5
20
24
29
35
f
2
3
4
3
5

Solution: Here, frequency table,
                       
x
f
cf
5
20
24
29
35
2
3
4
3
5
2
5
9
12
17

N = 17


            Total number of data (N) = 17         
Example 3: Solution


Example 4: Compute Q1 and Q3 from the following data.

Marks in maths
0-10
10-20
20-30
30-40
40-50
No. of students
5
20
10
15
7

Solution: Here, frequency table,
                       
Marks (x)
f
cf
0-10
10-20
20-30
30-40
40-50
5
20
10
15
7
5
25
35
50
57

N = 57


            Here, N = 57                       
Example 4: Solution


You can comment your questions or problems regarding the quartiles here.


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