Quartiles

Quartiles are set of 3 values(points) that divides a set into four equal parts(quarters).

The three points are as follows:

  • The given set should be arranged in order(either ascending or descending).
  • Median (Q2) is the middle value of the given set.

          Q2 = 1/2(n+1)th value, where n is the total number of elements in the given set.

  • Lower quartile(Q1) is the middle value of the lower half of given set.

           Q1= 1/4(n+1)th value,  where n is the total number of elements in    the set.

  • Upper quartile (Q3) is the median of the upper half of the given set.

         Q3 = 3/4(n+1)th value, where n is the total number of elements in the given set.

Example 1. Find the  quartiles of the following set {3,2,5,4,4,7,2}.

Solution:

  • Let us arrange in ascending order. 2,2,3,4,4,5,7.
  • Since there are 7 elements in the set, the

 lower quartile Q1 = (7+1)/4th value,

                        = 8/4thvalue

                        = 2nd value of the given set.

               So Q1 = 2.

  • Median = (7+1)/2 th value

                     = 8/2th value

                     = 4th value of the set

             So Q2 =  4

  • Upper quartile Q3 = 3/4(n+1)th value

                                   = 3/4(8) th value

                                   = 6 th value of the given set

                          So Q3 = 5.


Example 2: Find the median, upper quartile, and lower quartile of the given set {21, 25 22, 22, 20, 26, 23, 24, 24}

Solution:

  • Arrange the given set in order

          20, 21, 22, 22, 23, 24, 24, 25, 26.

  • Since there are 9 elements in the set n=9.
  • The lower quartile Q1 = (9+1)/4 th value

                                        = 10/4 th value

                                        = 2.5 th value, since we can not take the 2.5th value

we will take Q1 as the average of 2nd and 3rd value

                                  Q1  = Average of 2nd and 3rd value

                                        = (21+22)/2

                                        = 21.5

  • The median Q2         = (9+1)/2 th valule

                                       =   10/2 th value

                                       =  5th value

                           Q2        =  23

  • The upper quartile Q3 = 3(9+1)/4 th value

                                         = 3/4(10)th value

                                         = 7.5 th value

                                        = Average of 7 and 8th value

                                        = (24+25)/2

                                 Q3   = 24.5


                                         Basic statistics

                                           





Quartiles to Basic statistics