Find the Quarties Q1 Q2 Q3 for the data set below 68 77 85 5

Find the Quarties Q1, Q2, Q3 for the data set below:

68 77 85 54 49 69 58 67 57 56 86 57 87 59 55 61

Solution

given data set is ascending order is 49 54 55 56 57 57 58 59 61 67 68 69 77 85 86 87

Q₁=Value of ((n+1)/4)th item
                  =Value of ((16+1)/4)th item
                  =Value of (4.25)th item
                  =4th item+0.25(5th item4th item)=56+0.25(5756)
            Q₁= 56.25

Q₂= median = 2((n+1)/4)th item

        = (2(16+1)/4)th item

        = 8.5 th item = 8th item + 0.5(9 th item - 8th item)=59 +0.5(61-59)=60
            Q₃=Value of (3(n + 1)/4)th item
                  =Value of (3(16 + 1)/4)th item
                  =Value of (12.75)th item
                  =12th item+0.75(13th item12th item)=69+0.75(7769)
            Q₃=69+6 = 75

Q₄ = maximum = 87