Question

Find the median of the following observations : 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?

Answer 1

Given numbers are
46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33
Arrange in increasing order
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
n =1(odd)

∴ Median = `((n+1)/2)^(th)value`

              =  `((11+1)/2)^(th)value`

               = `6^(th) value = 58`

               If 92 is replaced by 99 and 41 by 43
              Then, the new values are
              33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
              ∴ n =11 (odd)

New median `((n+1)/2)^(th)`value

                 =  `((11+1)/2)^(th)`value

                 = `6^(th)value`

                  = 58 .